Searching for long-lived particles beyond the Standard Model at the Large Hadron Collider

Motivated by our over-arching UV frameworks, we can identify a minimal set of interesting production modes for LLPs. Schematic diagrams for each production mode are shown in figure 3. These production modes determine LLP signal rates both by relating the LLP production cross section to meaningful theory parameters such as gauge charges or Higgs couplings, and by determining the kinematic distribution of the LLP. Additionally, a given production mechanism also makes clear predictions for the number and type of prompt objects accompanying the LLP(s). These prompt AOs can be important for both triggering on events with LLPs and for background rejection, particularly when the LLP has a low mass or decays purely hadronically, and they can be either SM states (leptons, ${{/}\!\!\!\!{E}}_{{\rm{T}}}$, tagging jets) or BSM objects such as $Z^{\prime}$ or dark photons [157, 184, 185].

• Direct-pair production (DPP): Here the LLP is dominantly pair-produced non-resonantly from SM initial states. This is most straightforwardly obtained when the LLP is charged under a SM gauge interaction. In this case, an irreducible production cross section is then specified by the LLP gauge charge and mass. Such continuum DPP can also occur in the presence of a (heavy, virtual) mediator (e.g. an initial quark−antiquark pair may exchange a virtual squark to pair produce bino-like neutralinos); in this case the production cross section is essentially a free parameter, as it is determined by the unknown heavy mediator masses and couplings.
• Heavy parent (HP): The LLP is produced in the decays of on-shell HP particles that are themselves pair produced from the pp initial state. The production cross section is essentially a free parameter, and is indirectly specified by the gauge charges and masses of the HP particles. Heavy-parent production gives very different kinematics for the LLP than DPP, and often produces additional prompt AOs in the rapid cascade decays of the parents.
• Higgs (HIG): Here the LLP is produced through its couplings to the SM-like Higgs boson. This case has an interesting interplay of possible production modes. The dominant production is via gluon fusion, which features no AOs beyond gluon ISR. Owing to its role in electroweak symmetry breaking, however, the Higgs has associated production modes (VBF, VH), each with its own characteristic features. The best prospects for discovery are for LLP masses below m_h/2, in which case the LLPs can be in decays of the on-shell SM-like Higgs boson. Higher-mass LLPs can still be produced via an off-shell Higgs, albeit at substantially lower rates [26, 186]. The LLP can be pair produced or singly produced through the Higgs portal depending on the model; an LLP X can also be produced in association with ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ via $h\to {XX}+{{/}\!\!\!\!{E}}_{{\rm{T}}}$ or $h\to X+{{/}\!\!\!\!{E}}_{{\rm{T}}}$. The cross section (or, equivalently, the Higgs branching fraction into the LLP) is a free parameter of the model. The Higgs mass can also be taken as a free parameter: there exist many theories that predict new exotic scalar states (such as the singlet-scalar extension to the SM [119]), and these new scalars can be produced in the same manner as the SM Higgs.
• Heavy resonance (RES): Here the LLP is produced in the decay of an on-shell resonance, such as a heavy $Z^{\prime}$ gauge boson initiated by $q\bar{q}$ initial state. Note that production via an off-shell resonance is kinematically similar to the DPP mode. As with HIG, the LLP can be pair produced or singly produced (potentially in association with ${{/}\!\!\!\!{E}}_{{\rm{T}}}$). In RES models, ISR is the dominant source of prompt AOs. Models with new heavy scalars could conceivably fall into either RES or HIG; the main determining factor according to our organizational scheme is whether the scalar possesses Higgs-like production modes such as VBF and VH. Note that heavy resonance decays to SM particles also occur in these models, and searches for such resonances [187–193] may complement the sensitivity for decays to LLPs.
• Charged current: In models with weak-scale RHNs, the LLP can be produced in the leptonic decays of $W/W^{\prime}$. Single production is favored. Prompt charged leptons from the CC interaction are typical prompt AOs.

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It is important to note that each of the above production mechanisms has its own 'natural' set of triggers to record the signal. For example, HIG production can be accompanied by forward jets or leptons that are characteristic of VBF or VH production. Similarly, CC production often results in prompt charged leptons, while HP production comes with AOs from the HP decay. However, the reader should be cautioned that this does not necessarily mean that the 'natural' trigger is optimal for a particular signal. For example, the HIG modes suggest the use of VBF- or VH-based triggers, but if the LLP decays leptonically, it might be more efficient to trigger on the lepton from the LLP decay. Thus, the final word on which trigger is most effective for a given simplified model depends on the production mode as well as the nature and kinematics of the LLP decay. The prompt AOs of each production mode could still, however, be used to extend sensitivity to the model (see section 6.3).

We also comment that some models may span several production modes. For example, a charged LLP that is part of an electroweak multiplet and nearly degenerate with a stable, neutral component [63–65, 99, 128–130, 194, 195] gives both DPP signatures (via ${pp}\to {\chi }^{+}{\chi }^{-}$) and CC production (via associated production ${pp}\to {\chi }^{\pm }{\chi }^{0}$). Comprehensive coverage of each of the above production modes will allow for a conservative determination of sensitivity for models that span many production modes.

We now list a characteristic set of LLP decay modes. As we attempt to construct a minimal, manageable set of decay-mode building blocks, it is important to bear in mind that a given experimental search for LLPs can frequently be sensitive to a variety of possible LLP decay modes. As a result, it is not always necessary to perform separate searches for each possible decay mode as might otherwise be needed for prompt signatures.

The fact that LLP searches can be sensitive to many LLP decay modes is, in part, because LLPs that decay far from the collision point offer fewer avenues for particle identification. For example, for an LLP decaying inside of the calorimeter, most decay products are reconstructed as missing energy, or an energy deposition in the calorimeter. Consequently, particle identification criteria are typically relaxed in comparison to requirements on searches without displaced objects. Indeed, these 'loose' collider objects can differ significantly from the corresponding 'tight' prompt objects. This leads to more inclusive analyses that can cover a wider range of signatures with a single search.

Additionally, backgrounds for LLP searches are often small; for a comprehensive discussion of backgrounds to LLP searches, see chapter 4. As a result, tight identification and/or reconstruction criteria typically found in exclusive prompt analyses are no longer needed to suppress backgrounds. For example, ATLAS has a displaced vertex (DV) search sensitive to di-lepton and multi-track vertices that is relatively inclusive with respect to other objects originating from near the DV [196]. Similarly, CMS has an analysis sensitive to events with one each of a high-impact-parameter muon and electron without reconstructing a vertex or any other objects [197]. For these examples, the backgrounds are sufficiently low that other requirements may be relaxed and the specific decay mode of the LLP may not be too important so long as certain objects (such as muons) are present or the decay occurs in a specific location. An even more extreme example in this regard is the search for highly-ionizing tracks sensitive to electrically and color-charged LLPs. While the searches are primarily targeted to detector-stable particles (HSCPs or R-hadrons) they can also be used to probe intermediate lifetimes for which only a certain fraction of LLPs traverse the tracker before decaying (see e.g. [142]). Both because of low backgrounds as well as modified particle identification criteria compared to prompt searches, LLP searches can often be inclusive and therefore covered by a more limited range of simplified models.

In some cases, however, the topology of a decay does matter. One potentially important factor that influences the sensitivity of a search to a particular model is whether the LLP decays into two SM objects versus three, because the kinematics of multi-body decay are distinct from two-body decay and this may affect the acceptance of particular search strategies. An additional simplified model featuring a three-body decay of the LLP may consequently be needed to span the space of signatures.

Below, we describe an irreducible set of decay modes that can be used to characterize LLP signatures for various LLP charges (including neutral, electrically charged, and color charged). For each, we also provide an explicit example for how the decay would appear in a particular UV model. We emphasize that the following decay modes are loosely defined with the understanding that their signatures are also representative of similar, related decay modes; for example 2j or $2j+{{/}\!\!\!\!{E}}_{{\rm{T}}}$ can also be proxies for 3j because searches for multi-body hadronic LLP decays can be sensitive to both and typically do not require reconstruction of a third jet. It should also be noted that we are not recommending searches to be optimized to the exact, exclusive decay mode because that could suppress sensitivity to related but slightly more complicated LLP decays.

• Di-photon decays: The LLP can decay resonantly to γγ (like in Higgs-portal models or left−right symmetric models [198]) or to γγ + invisible (in DM models). This latter mode stands as a proxy for other γγ + X decays where the third object is not explicitly reconstructed, although whether X is truly invisible can influence the triggers used. Example: a singlino decaying to a singlet (which decays to γγ) and a gravitino in Stealth SUSY [54].
• Single-photon decays: The LLP decays to γ + invisible (like in SUSY models). The SUSY model mandates a near-massless invisible particle, while other models (such as DM theories [134, 156]) allow for a heavy invisible particle. Example: a bino decaying to photon plus gravitino in gauge-mediated models of SUSY breaking [199].
• Hadronic decays: The LLP can decay into two jets (jj) (like in Higgs and gauge-portal models, or RPV SUSY), jj + invisible (SUSY, DM, or neutrino models), or j + invisible (SUSY). Here, 'jet' (j) means either a light-quark parton, gluon, or b-quark. This category also encompasses decays directly into hadrons (for example, LLP decay into π⁺ plus an invisible particle [63–65]). Example: a scalar LLP decaying to $b\bar{b}$ due to mixing with the SM Higgs boson, as in models of neutral naturalness [13, 14, 118].
• Semi-leptonic decays: The LLP can decay into a lepton + 1 jet (such as in leptoquark (LQs) models) or 2 jets (like in SUSY or neutrino models). Example: a RHN decaying to a left-handed lepton and an on- or off-shell hadronically decaying W boson (or $W^{\prime}$ boson in a left−right symmetric model) [163].
• Leptonic decays: The LLP can decay into ${{\ell }}^{+}{{\ell }}^{-}(+\mathrm{invisible})$, or ${{\ell }}^{\pm }+\mathrm{invisible}$ (as in Higgs-portal, gauge-portal, SUSY, or neutrino models). Here the symbol ℓ may be any flavor of charged lepton, but the decays are lepton flavor-universal and (for ${{\ell }}^{+}{{\ell }}^{-}$ decays) flavor-conserving. Example: a wino decaying to a neutralino and an on- or off-shell leptonic Z boson in SUSY [55].
• Flavored leptonic decays: The LLP can decay into ℓ_α + invisible, ${{\ell }}_{\alpha }^{+}{{\ell }}_{\beta }^{-}$ or ${{\ell }}_{\alpha }^{+}{{\ell }}_{\beta }^{-}+\mathrm{invisible}$ where flavors $\alpha \ne \beta$ (as in SUSY or neutrino models). Example: a neutralino decaying to two leptons and a neutrino in R-parity-violating SUSY [55]; or a RHN decaying to two leptons and a neutrino [200].

In all cases, both the LLP mass and proper lifetime are free parameters. Therefore, the case of detector-stable particles is automatically included by taking any of the above decay modes and taking the lifetime to infinity¹⁴⁵ . We emphasize that, depending on the location of the LLP within the detector, these decay modes may or may not be individually distinguishable: a displaced di-jet decay will look very different from a displaced di-photon decay in the tracker, but nearly identical if the decay occurs in the calorimeter. The goal here is to identify promising channels (as distinct from detector signatures).

As an example of how the above-listed decay modes cover the most important experimental signatures, we consider a scenario of an LLP decaying to top quarks. This scenario is very well motivated (for instance, with long-lived stops in SUSY) and might appear to merit its own decay category of an LLP decaying to one or more top quarks. However, the top quark immediately decays to final states that are covered in the above list, giving an effective semileptonic decay mode ($t\to b{{\ell }}^{+}\nu$) and a hadronic decay mode ($t\to {bjj}$) of the LLP. Similarly, LLP decays to four or more final states are typically covered by the above inclusive definitions of decay modes; this provides motivation not to over-optimize experimental searches to the specific, exclusive features of a particular decay mode.

While it would be ideal to have separate experimental searches for each of the above decay modes (when distinguishable), it is rare for specific models to allow the LLP to decay in only one manner; as in the example of an LLP decaying to a top quark, a number of decay modes typically occur with specific predictions for the branching fractions. As another example, if the LLP couples to the SM via mixing with the SM Higgs boson, then the LLP decays via mass-proportional couplings giving rise to b- and τ-rich signatures. If, instead, the LLP decays through a kinetic mixing as in the case of dark photons or Z bosons, then the LLP can decay to any particle charged under the weak interactions, giving rise to a relatively large leptonic branching fraction in addition to hadronic decay modes. This allows some level of prioritization of decay modes based on motivated UV-complete models; for example, the Higgs-portal model prioritizes searches for heavy-flavor quarks and leptons in LLP decay, while the gauge-portal model prioritizes searches for electrons and muons in LLP decay. Ultimately, however, it is desirable to retain independent sensitivity to each individual decay mode as much as possible. Indeed, for each decay mode listed above, models exist for which the given decay mode would be the main discovery channel.

Invisible final-state particles: Where invisible particles appear as products of LLP decays, additional model dependence arises from the unknown mass of the invisible particle. The invisible particle could be a SM neutrino, DM, an LSP in SUSY, or another BSM particle. The phenomenology depends strongly on the mass splitting, ${\rm{\Delta }}\equiv {M}_{\mathrm{LLP}}-{M}_{\mathrm{invisible}}$. If Δ ≪ M_LLP (i.e. M_LLP ∼ M_invisible), the spectrum is compressed and the visible decay products of the LLP are soft. This could, for instance, lead to signatures such as disappearing tracks (DTs) or necessitate the use of ISR jets to trigger on the LLP signature. If the mass splitting is large, ${M}_{\mathrm{invisible}}\ll {M}_{\mathrm{LLP}}$, then the signatures lose their dependence on the invisible particle mass.

We suggest three possible benchmarks: a compressed spectrum with Δ ≪ M_LLP (example: a nearly degenerate chargino-neutralino pair, giving rise to soft leptons or DTs [63–65, 99, 128–130, 194, 195]); a massless invisible state, Δ = M_LLP (example:a next-to-lightest SUSY particle (NLSP) decaying to SM particles and a massless gravitino in gauge-mediated SUSY breaking (GMSB) [112, 201–206]); and an intermediate splitting corresponding to a democratic mass hierarchy, Δ ≈ M_LLP/2 (example: NLSPs in mini-split SUSY [57, 58, 96]).

The simplified model channels for neutral LLPs are shown in table 1, where X indicates the LLP.

Table 1.  Simplified model channels for neutral LLPs. The LLP is indicated by X. Each row shows a separate production mode and each column shows a separate possible decay mode, and therefore every cell in the table corresponds to a different simplified model channel of (production) × (decay). We have cross-referenced the UV models from section 2.2 with cells in the table to show how the most common signatures of complete models populate the simplified model space. The asterisk (*) shows that the model definitively predicts missing energy in the LLP decay. A dagger (${}^{\dagger }$) indicates that this particle production × decay scenario is not present in the simplest and most minimal implementations or spectra of the umbrella model, but could be present in extensions of the minimal models. When two production modes are provided (with an 'or'), either simplified model can be used to simulate the same simplified model channel.

	Decay
Production	$\gamma \gamma (+\mathrm{inv}.)$	$\gamma +\mathrm{inv}.$	${jj}(+\mathrm{inv}.)$	${jj}{\ell }$	${{\ell }}^{+}{{\ell }}^{-}(+\mathrm{inv}.)$	${{\ell }}_{\alpha }^{+}{{\ell }}_{\beta \ne \alpha }^{-}(+\mathrm{inv}.)$
DPP: sneutrino pair	${}^{\dagger }$	SUSY	SUSY	SUSY	SUSY	SUSY
or neutralino pair
HP: squark pair, $\tilde{q}\to {jX}$	${}^{\dagger }$	SUSY	SUSY	SUSY	SUSY	SUSY
or gluino pair $\tilde{g}\to {jjX}$
HP: slepton pair, $\tilde{{\ell }}\to {\ell }X$	${}^{\dagger }$	SUSY	SUSY	SUSY	SUSY	SUSY
or chargino pair, $\tilde{\chi }\to {WX}$
HIG: $h\to {XX}$	Higgs, DM*	${}^{\dagger }$	Higgs, DM*	RHν	Higgs, DM*	RHν*
or $\to {XX}+\mathrm{inv}.$					RHν*
HIG: $h\to X+\mathrm{inv}.$	DM*, RHν	${}^{\dagger }$	DM*	RHν	DM*	${}^{\dagger }$
RES: $Z(Z^{\prime} )\to {XX}$	$Z^{\prime}$, DM*	${}^{\dagger }$	$Z^{\prime}$, DM*	RHν	$Z^{\prime}$, DM*	${}^{\dagger }$
or $\to {XX}+\mathrm{inv}.$
RES: $Z(Z^{\prime} )\to X+\mathrm{inv}.$	DM	${}^{\dagger }$	DM	RHν	DM	${}^{\dagger }$
CC: $W(W^{\prime} )\to {\ell }X$	${}^{\dagger }$	${}^{\dagger }$	RHν*	RHν	RHν*	RHν*

In our initial proposal, which is the first iteration of the simplified model framework, it is sufficient to consider as 'jets' all of the following: j = u, d, s, c, b, g. It is worth commenting that b-quarks pose unique challenges and opportunities. Since b-quarks are themselves LLPs, they appear with an additional displacement relative to the LLP decay location. They also often give rise to soft muons in their decays, which could in principle lead to additional trigger or selection possibilities. However, these subtleties can be addressed in further refinements of the simplified models; we discuss this further in section 2.6. Similarly, we consider e, μ, and τ to be included in the broad category of 'leptons', with the proviso that searches should be designed where possible with sensitivity to each.

When multiple production modes are specified in one row of the table, this means that multiple especially well-motivated production channels give rise to similar signatures. Typically only one of these simplified model production modes will actually need to be included when developing and assessing sensitivity of an experimental search, but we sometimes include multiple different production modes as individuals may variously prefer one over the other.

In each entry of the table, we indicate which umbrella category of well-motivated UV models (section 2.2) can predict a particular $(\mathrm{production})\times (\mathrm{decay})$ mode. An asterisk (*) on the umbrella model indicates that ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ is required in the decay. A dagger (${}^{\dagger }$) indicates that this particle production × decay scenario is not present in the simplest and most minimal implementations or spectra of the umbrella model, but could be present in extensions of the minimal models. While the HIG production signatures are best-motivated for the SM-like 125 GeV Higgs, exotic Higgses of other masses can still have the same production modes and so m_H can be taken as a free parameter.

We remind the reader that the production modes listed in table 1 encompass also the associated production of characteristic prompt objects. For example, the Higgs production modes not only proceed through gluon fusion, but also through VBF and VH production, each of which results in associated prompt objects such as forward jets in VBF, and leptons or ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ in VH. All of the production modes listed in table 1 could be accompanied by ISR jets that aid in triggering or identifying signal events. It is therefore important that searches are designed to exploit such prompt AOs whenever they can improve signal sensitivity, especially with regard to triggering.

To demonstrate how to map full models onto the list of simplified models (and vice-versa), we consider a few concrete cases. For instance, if we consider a model of neutral naturalness where X is a long-lived scalar that decays via Higgs mixing (for instance, X could be the lightest quasi-stable glueball), then the process where the SM Higgs h decays via $h\to {XX}$, $X\to b\bar{b}$ would be covered with the HIG production mechanism and a di-jet decay. Entirely unrelated models, such as the case where X is a bino-like neutralino with RPV decays $h\to {XX}$, $X\to {jjj}$ could be covered with the same simplified model because most hadronic LLP searches do not have exclusive requirements on jet multiplicity. Similarly, a hidden-sector model with a dark photon, $A^{\prime}$, produced in $h\to A^{\prime} A^{\prime}$, $A^{\prime} \to f\bar{f}$ would also give rise to the di-jet signature when f is a quark, whereas it would populate the ${{\ell }}^{+}{{\ell }}^{-}$ column if f is a lepton. Finally, a scenario with multiple hidden-sector states X₁ and X₂, in which X₂ is an LLP and X₁ is a stable, invisible particle, could give rise to signatures like $h\to {X}_{2}{X}_{2}$, ${X}_{2}\to {X}_{1}{jj}$ that would be covered by the same HIG production, hadronic-decay simplified model; however, we see how ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ can easily appear in the final state, and that the LLP decay products may not be entirely hadronic. Therefore, the simplified models in table 1 can cover an incredibly broad range of signatures, but only if searches are not overly optimized to particular features such as ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ and LLPs decaying entirely visibly (which would allow reconstruction of the LLP mass)¹⁴⁶ .

For an electrically charged LLP, we need to consider far fewer production modes because of the irreducible gauge production associated with the electric charge. We still consider the additional possibility of a HP scenario where the parent has a QCD charge, as this could potentially dominate the production cross section, see e.g. [95]. We summarize our proposals in table 2.

Table 2.  Simplified model channels for electrically charged LLPs such that $| Q| =1$. The LLP is indicated by X. Each row shows a separate production mode and each column shows a separate possible decay mode, and therefore every cell in the table corresponds to a different simplified model channel of (production) × (decay). We have cross-referenced the UV models from section 2.2 with cells in the table to show how the most common signatures of complete models populate the simplified model space. The asterisk (*) shows that the model definitively predicts missing energy in the LLP decay. A dagger (${}^{\dagger }$) indicates that this particle production ×  decay scenario is not present in the simplest and most minimal implementations or spectra of the umbrella model, but could be present in extensions of the minimal models. When two production modes are provided (with an 'or'), both production simplified models can be used to cover the same experimental signatures.

	Decay
Production	${\ell }+\mathrm{inv}.$	${jj}(+\mathrm{inv}.)$	${jj}{\ell }$	${\ell }\gamma$
DPP: chargino pair	SUSY	SUSY	SUSY	${}^{\dagger }$
or slepton pair	DM*	DM*
HP: $\tilde{q}\to {jX}$	SUSY	SUSY	SUSY	${}^{\dagger }$
	DM*	DM*
RES: $Z^{\prime} \to {XX}$	Z', DM*	Z', DM*	Z'	${}^{\dagger }$
CC: $W^{\prime} \to X+\mathrm{inv}.$	DM*	DM*	RHν	${}^{\dagger }$

Note that we group all resonant production into the $Z^{\prime}$ simplified model. The reason is that the SM Higgs cannot decay into two on-shell charged particles due to the model-independent limits from LEP on charged particle masses, M ≳ 75−90 GeV (see, for example, [207]); because of this lower limit on the LLP mass, it is less important to use AOs for triggering and reconstructing charged LLP signatures than for neutral LLPs. Additionally, there are fewer allowed decay modes because of the requirement of charge conservation.

For concreteness, we recommend using $| Q| =1$ as a benchmark for charged LLPs for the purpose of determining allowed decay modes. Although other values of Q are possible, these often result in cosmologically stable charged relics or necessitate different decay modes than those listed here. Additionally, LLPs with $| Q| =1$ are motivated within SUSY [63–65, 208–210] and within Type-III seesaw models of neutrino masses [211–214]. We note that there exist already dedicated searches for heavy quasi-stable charged particles with non-standard charges [215, 216]. Because such searches are by construction not intended to be sensitive to the decays of the LLP, the existing models are sufficient for characterizing these signatures and they do not need to be additionally included in our framework.

For massive particles with $| Q| =1$ with intermediate or large lifetimes such that the LLP traverses a significant part (or all) of the tracker, the highly ionizing track of the LLP provides a prominent signature. This can be exploited for an efficient suppression of backgrounds while keeping identification and/or reconstruction criteria as loose and, hence, as inclusive as possible. In particular, for decay-lengths of the order of or larger than the detector size, the signature of highly ionizing tracks and anomalous time of flight (TOF) (i.e. searches for HSCPs; see sections 3.5 and 6.4.1) constitute an important search strategy covering a large range of lifetimes present in the parameter space of theoretically motivated models. While the searches for HSCPs are largely inclusive with respect to additional objects in the event, they depend strongly on the velocity of the LLP. For β → 1 one loses the discriminating power against minimally ionizing particles, while for small velocities, β ≲ 0.5, the reconstruction becomes increasingly difficult due to timing issues. It is therefore important to include the HP production scenario which covers a much larger kinematic range than direct production alone and which may feature a much wider range of signal efficiencies than the DPP scenario [97].

While the signatures in table 2 form a minimal set, they also encompass some scenarios that merit special comment. One of these is the DT signature [63–65, 99, 128–130, 194, 195], in which a charged LLP decays to a nearly degenerate neutral particle. The lifetime is long in this scenario due to the tiny mass splitting between the two states. Formally, these are included in the chargino or slepton DPP modes in table 2 with decays to ℓ + inv. or $q\bar{q}^{\prime} +\mathrm{inv}.$ taken in the limit where the splitting between the charged LLP and the invisible final state is of ${ \mathcal O }(200\,\mathrm{MeV})$. In the case of a hadronic decay, X decays to a soft pion that is very challenging to reconstruct and so the track simply disappears. This is an important scenario that is already the topic of existing searches [217, 218]. As the degeneracy between the charged LLP and the neutral state is relaxed, other signatures are possible; this parameter range is well motivated both by SUSY and DM models with coannihilation [98, 136, 137].

Finally, we comment on the challenges of simulating the charged LLP simplified models. Because the LLP bends and interacts with detector material prior to its decay, the simulation of the LLP propagation is important in correctly modeling the experimental signature. The subsequent decay of the LLP must either be hard-coded into the detector simulation, or allow for an interface with programs such as Pythia 8 to implement the decays. We discuss the challenges of simulating signals for LLPs with electric or color charge in section 2.5.2.

An LLP charged under QCD is more constrained than even electrically charged LLPs. Because of the non-Abelian nature of the strong interactions, the gauge pair-production cross section of the LLP is specified by the LLP mass and its representation under the color group, SU(3)_C. We do not consider LLP production via a HP particle because that cross section is unlikely to dominate the total production rate at the LHC relative to DPP. The simplified model channels are provided in table 3.

Table 3.  Simplified model channels for LLPs with color charge. The LLP is indicated by X. Each row shows a separate production mode and each column shows a separate possible decay mode, and therefore every cell in the table corresponds to a different simplified model channel of (production) × (decay). We have cross-referenced the UV models from section 2.2 with cells in the table to show how the most common signatures of complete models populate the simplified model space. A dagger (${}^{\dagger }$) indicates that this particle production × decay scenario is not present in the simplest and most minimal implementations or spectra of the umbrella model, but could be present in extensions of the minimal models. When two production modes are provided (with an 'or'), both production simplified models can be used to cover the same experimental signatures.

	Decay
Production	$j+\mathrm{inv}.$	${jj}(+\mathrm{inv}.)$	$j{\ell }$	$j\gamma$
DPP: squark pair	SUSY	SUSY	SUSY	${}^{\dagger }$
or gluino pair

A complication of the QCD-charged LLP is that the LLP hadronizes prior to its decay, forming an R-hadron bound state. The modeling of hadronization and subsequent propagation is directly related to many properties of the long-lived parton, such as electric charge, flavor, and spin. Event generators such as Pythia 8 have routines [219, 220] to simulate LLP hadronization, although it is unclear how precise these predictions are. For a point of comparison, using the default settings of Pythia 8 yields an estimate of the neutral R-hadron fraction from a gluino (color-octet fermion, $\tilde{g}$) of approximately 54%, while the neutral R-hadron fraction for a stop (scalar top partner) is estimated to be 44% [96]. After hadronization, the charge of the R-hadron may change as it passes through the detector. For instance, some estimates [221, 222] suggest that heavy, color-octet gluinos $\tilde{g}$ would predominantly form mesons (e.g. $(u\tilde{g}\bar{d})$) at first. They eventually drop to the lower-energy neutral singlet baryon $\tilde{{\rm{\Lambda }}}=(\tilde{g}{uds})$ state when interacting with the protons and neutrons within the calorimeters.

The modeling of LLP hadronization and propagation is crucial to designing searches for color-charged LLPs and assessing their sensitivity. For example, only the charged R-hadrons can be found in HSCP search; if the LLP charge changes as it passes through the detector, HSCP searches may have limited sensitivity. To take this into account, the experimental searches include both tracker-only or tracker + calorimeter signal regions [4, 223], which enhances sensitivity to the scenario in which R-hadrons lose their charge by the time they reach the calorimeters.

Because no R-hadrons have been discovered to date and hence their properties cannot be directly measured, R-hadron modeling in detector simulations is challenging. We discuss the challenges of simulating the propagation and decays of LLPs with color charge in section 2.5.2.

In order to reproduce the simplified model channels of section 2.3, we need a collection of models that:

• Includes additional gauge bosons and scalars to allow vector- and scalar-portal production of LLPs (RES and HIG).
• Includes new gauge-charged fermions and scalars to cover direct and simple cascade production modes of LLPs (DPP and HP).
• Includes a RHN-like state with couplings to SM neutrinos and leptons (CC).
• Recommended, but optional: Allows for the decays of the LLP particle through all of the decay modes listed in section 2.3, either through renormalizable or higher-dimensional couplings. If couplings that allow LLP decay are included in the UFO model, then the decays can be performed directly at the matrix-element level in programs such as MadGraph5_aMC@NLO [226] and accompanying packages such as MadSpin [227]. Alternatively, it is possible for neutral LLPs to simulate the production and decay as a single process; in such cases, numerical instabilities sometimes arise, for which dedicated event generators are needed [49]. If the couplings needed for LLP are not in the UFO model, then LLPs can be left stable at the matrix-element level and decays implemented via Pythia 8 [219, 220], which allows for the straightforward implementation of decays according to a phase-space model, but does not correctly model the angular distribution of decay products. Instructions for implementing decays in Pythia are included with the model library files.

Fortunately, an extensive set of UFO models is already available for simulating the production of BSM particles. We note that extensions or generalizations of only three already-available UFO models are needed at the present time; the SUSY models in particular can cover many of the simplified models since they contain an enormous collection of new fermions and scalars. We also provide an optional fourth model, the Hidden Abelian Higgs Model, that can be helpful to simulate HIG and ZP theories.

• 1.  
  The MSSM: The use of this model is motivated by and allows for the simulation of SUSY-like theories. The model contains a whole host of new particles with various gauge charges and spins. Therefore, an MSSM-based model allows for the simulation of many of the simplified model channels. In particular, we note that existing UFO variants of the MSSM that include gauge-mediated supersymmetry breaking (GMSB) couplings (including decays to light gravitinos), R-parity violation (making unstable the otherwise stable LSPs [55, 110, 111]), and the phenomenological MSSM (pMSSM) [228, 229] already cover most of the SUSY-motivated LLP scenarios. In some cases, the model is modified to give direct couplings between the Higgs states and gluons/photons.
• 2.  
  The left–right symmetric model (LRSM): This UFO model is best for simulating UV theories with right-handed neutrinos (RHν). The UFO model supplements the SM by an additional SU(2)_R symmetry, which gives additional charged and neutral gauge bosons. The model is available in the simplified models library and contains a RHN which is the typical LLP candidate. The LLP can be produced via SM W, Z, or via the new gauge and Higgs bosons (both charged and neutral) present in the theory¹⁴⁸ . The LRSM therefore contains many of the charged and neutral current LLP production processes outlined in section 2.4.1.
• 3.  
  Dark-matter simplified models (DMSM): These UFO models are best for simulating UV theories in the DM class. These UFO models have been created by the LHC DM working group [86]. They typically consist of a new BSM mediator particle (such as a scalar of a $Z^{\prime}$) coupled to invisible DM particles. The UFO models can either be modified to include an unstable LLP, or else the otherwise stable 'DM' particle can be decayed via Pythia. The utility and applicability of the DM simplified model framework to LLPs has already been demonstrated with a detailed proposal and study of classes of DM simplified models for LLPs [100]. These models are particularly good for simulating LLP production via a heavy resonance (RES), and can also simulate continuum production of LLPs in the limit where the mediator is taken to be light and off-shell (DPP).
• 4.  
  (Optional) The hidden abelian Higgs model (HAHM): This UFO model contains new scalars and gauge bosons and so can be used to simulate both Higgs-portal and gauge-portal (ZP) theories. The model consists of the SM supplemented by a 'hidden sector' consisting of a new U(1) gauge boson and a corresponding Higgs field. The physical gauge and Higgs bosons couple to the SM via kinetic and mass mixing, respectively. The HAHM allows for straightforward simulation of Higgs-portal production of LLPs, as well as $Z^{\prime}$ models and many hidden sector scenarios. The UFO implementation is from [230].

If additional decay modes are needed beyond those in the specified simplified models, then the library can be updated to include the new couplings mediating the decay. Alternatively, the LLPs can be left stable at parton level and decayed in event generators such as Pythia.

A detailed list of processes that can be used to simulate each simplified model channel is provided in the appendix. The primary purpose of the library is to be used to simulate events for determining acceptances, and, as a result, the signal cross section is not important. Thus, for example, SM gauge interactions can be used as proxies for much weaker exotic interactions. Similarly, the spins of the particles are generally of subdominant importance: replacing the direct production of a fermion with the direct production of a scalar will not fundamentally alter the signature. As long as results are expressed in terms of sensitivity to cross sections and not couplings, the results can be qualitatively (and in many cases, quantitatively) applied to any similar production mode regardless of spin. However, we caution the reader that changing the spin of the LLP (or its parent) can change the angular distribution, and since in some cases LLP searches are typically more sensitive to aspects of event geometry than prompt searches, the second-order effects of spin could have more of an effect than for prompt simplified models.

Long-lived particles with electric or QCD charges interact with the detector material prior to decay, and their propagation through the detector must be correctly modeled. The propagation of both LLPs with color charge (in the form of R-hadrons) and electrically charged LLPs can be implemented in the Geant4 (G4) toolkit [231]. For example, routines exist to simulate the propagation of color-charged LLPs [232, 233]. G4 also includes routines that can implement N-body decays of LLPs using a phase-space model. This works fine for decays of LLPs to leptons, photons, invisible particles such as neutrinos, as well as exclusive hadronic decays.

However, G4 cannot implement decays to partons that subsequently shower and hadronize. One solution to this limitation is employed by CMS [234, 235] and ATLAS [236] in their searches for stopped LLPs. In these analyses, the signal simulation proceeds in two stages. During the first stage, the production of the LLP and its subsequent interactions with the detector are simulated. Once the stopping point of the LLP is determined, a new event is simulated including the LLP decay; the LLP decay products are then manually moved to the stopping point from the first stage. G4 is then run a second time to determine the efficiency for reconstructing the LLP decay signal.

It would be preferable to fully automate the simulation of decays of charged LLPs after propagation in G4. There exists in G4 a class called G4ExtDecayer, which can be used to implement decays by interfacing with an external generator. This class has been used to interface G4 with Pythia 6¹⁴⁹ . The interface with Pythia 6 has been used most recently to model LLP gluino propagation and decay in a search for DV and missing energy in ATLAS [237]. Work is ongoing to extend this functionality to Pythia 8 and to simplify the interface.

An additional challenge of simulating LLP decays is that, if the LLP undergoes a multi-body decay, generators such as Pythia use a phase-space model to implement the decays. If more accuracy is required, it may be preferable to use the full matrix element via generators such as MadGraph5 [226, 238]. If the matrix element is important for computing the decay of the LLP, then either an interface with MadGraph is needed to implement the decay prior to passing the vertex back to Pythia 8 for showering and hadronization, or matrix-element-based methods within the event generator itself must be used.

Because of the need to interface with G4 in simulating the decays of LLPs with electric or color charges, we do not at this point include such decay modes in our simplified model library. The decays of such LLPs will be most easily simulated via an interface with Pythia 8 once it is finalized.

Finally, we comment that LLPs can have even stranger propagation properties than LLPs with electric or color charges. For example, quirks are LLPs that are charged under a hidden-sector gauge interaction that confines at macroscopic scales [182]. Because the confinement scale can be just about any distance, quirks can have very unusual properties; as a specific example, if electrically charged quirk–antiquirk pairs are bound on the millimeter or centimeter level, they behave as an electric dipole and therefore do not leave conventional tracks that bend in the magnetic field. Other confinement scales give rise to different behaviors, such as meta-stable heavy charged particles and non-helical tracks [239, 240]. In scenarios where the quirks carry color charge, the quirks hadronize and can undergo charge-flipping interactions as they move through the detector. These quirk scenarios can be challenging to model, and no public code exists that allows for the propagation and interaction of quirks with the detector material; we encourage the collaborations to validate and release any internal software they may have to study the propagation of quirks (for more discussion, see the discussion of quirks in section 3.5)¹⁵⁰ .

The reconstruction of displaced tracks in the ATLAS ID [255] follows a two-step procedure. In the first iteration, the default track identification algorithm is applied, which uses hits in the pixel system, semiconductor tracker, and transition radiation tracker (TRT) to reconstruct tracks with a small impact parameter. The hits not associated to a track during the first pass are used in a second run of the track finder, with loose requirements on the transverse and longitudinal impact parameters (d₀ and z₀) and the number of silicon hits that are shared (or not shared) with another track. This two-step procedure is referred to as the large radius tracking (LRT) algorithm by the ATLAS collaboration. Applying the LRT procedure is CPU-intensive, and thus it is only run once per data-processing campaign, on a subset of specially-requested events [255].

In searches where the LLPs decay exclusively in the ID, standard triggers are used to select events with high-${p}_{{\rm{T}}}$ jets, ${{/}\!\!\!\!{E}}_{{\rm{T}}}$, or high-${p}_{{\rm{T}}}$ leptons [196, 237]. An ATLAS 13 TeV search [237] uses a standard ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ trigger and an offline requirement of ${{/}\!\!\!\!{E}}_{{\rm{T}}}$  > 250 GeV. The 8 TeV search [196] covers a larger range of topologies, and the event must have either ${{/}\!\!\!\!{E}}_{{\rm{T}}}$  > 180 GeV or contain four, five, or six jets with ${p}_{{\rm{T}}}\gt 90$, 65, or 55 GeV to pass the trigger. In both searches, the ID vertex is required to have at least 5 tracks and the invariant mass of the DV tracks to fullfil m_DV > 10 GeV. These searches are interpreted in the context of various SUSY scenarios involving gluinos or squarks decaying into leptons, jets and missing energy, namely R-parity-violating (RPV), general gauge mediation, and split SUSY. In the latter case R-hadrons¹⁵³ are considered. The particular LLP decay topology determines which trigger and analysis mode (specified by jet and lepton multiplicity, small/large ${{/}\!\!\!\!{E}}_{{\rm{T}}}$, etc) has the best sensitivity. The LLPs covered by these searches are typically high mass (≳ 100 GeV), and correspond to the direct-pair-production and HP production modes with hadronic decays (in the language of the simplified models presented in section 2). However, these searches do not have sensitivity to low-mass LLPs, especially those resulting from the Higgs, $Z^{\prime}$, or CC production portals and then decaying hadronically.

For LLPs decaying in the HCAL or MS, dedicated CalRatio and MuonRoI triggers are employed [246–248, 256], allowing the searches to place limited requirements on the non-displaced portion of the event. We describe these triggers in more detail shortly. The efficiency of these triggers is 50%–70% for decays within the relevant geometric detector region, and negligible outside of them (see figure 3 of [248]). The results of these analyses are interpreted in terms of a ${\rm{\Phi }}\to {ss}$ model, where Φ is a heavy scalar boson with 100 GeV < m_Φ < 1000 GeV and s is a long-lived, neutral scalar decaying to hadrons with branching fractions dictated by the Yukawa coupling. This can map to Higgs or $Z^{\prime}$ production modes and hadronic decay mode in the simplified models.

The CalRatio trigger selects events with at least one trackless jet that has a very low fraction of energy deposited in the ECAL¹⁵⁴ . These CalRatio jets are characteristic of an LLP that decays within or just before the HCAL. The 13 TeV analysis [246] requires two CalRatio jets, where the exact CalRatio criteria are determined using a series of machine learning techniques to optimally discriminate the displaced decay signature from QCD jets and beam-induced background. Using the simplified ${\rm{\Phi }}\to {ss}$ model with 125 GeV < m_Φ < 1000 GeV and 5 GeV < m_s < 400 GeV, good sensitivity is observed for cτ between 0.05 and 35 m, depending on the Φ and LLP masses. Notably, SM-like Higgs boson decays to LLP pairs are constrained below 10% branching ratio in the most sensitive lifetime ranges, with exact limits dependent on the LLP mass [246]. The 8 TeV result also requires two CalRatio jets, and shows sensitivity for 100 GeV < ${m}_{{\rm{\Phi }}}$ < 900 GeV and 10 GeV < m_s < 150 GeV [247].

The MuonRoI trigger selects events with clusters of L1 regions of interest (RoIs) in the MS that are isolated from activity in the ID and calorimeters. It is efficient for LLPs that decay between 3 and 7 m transversely or 5–13 m longitudinally from the PV, for LLP masses greater than 10 GeV. After trigger selection, the ATLAS analysis in question requires either two reconstructed DVs in the MS [257] or one ID vertex and one MS vertex [248]. This ID–MS combination provides increased sensitivity to shorter lifetimes than an analysis only considering MS vertices, and shows good sensitivity to 100 GeV < m_Φ < 900 GeV and 10 GeV < m_s < 150 GeV. Decays of a SM-like Higgs boson to LLP pairs are constrained below 1% in the most sensitive cτ regions (with cross section limits as low as 50 fb). The efficiency degrades for benchmarks with higher LLP boosts or very low mass LLPs, as fewer tracks are reconstructed. Another ATLAS search includes signal regions with only 1 DV in the MS, with sensitivity to SM-like Higgs decays to LLPs extending down to branching fractions of 0.1% [258]; this search also presents constraints on a wide range of models that helps facilitate reinterpretation for other BSM scenarios. In addition, a combination of the results from this search with the results from the 13 TeV CalRatio search was performed in [246] for the models common to both, and provides a summary of the ATLAS results for pair-produced neutral LLPs.

Recently, ATLAS presented a new study for hadronically decaying LLPs produced in association with a leptonically decaying Z boson [259]. In this analysis, the LLP decays inside of the HCAL. The use of lepton triggers on the associated Z decay products gives sensitivity to production of a single low-mass LLP, whereas other searches typically require 2 DVs; it is therefore an excellent example of the utility of prompt associated objects in obtaining sensitivity to low-mass LLPs. The model constraints are expressed in terms of a Higgs portal model where the SM-like Higgs decays to a bosonic LLP.

With the exceptions of [196, 237, 259], which require prompt activity in addition to the DV and have comparatively high trigger thresholds, the ATLAS all-hadronic analyses require two DVs, and thus are insensitive to models that produce a single DV inside the detector¹⁵⁵ .

The CMS analyses [249–251] are based on a dedicated offline displaced jet tagging algorithm using tracker information to identify pairs of displaced jets. The triggers used here are based on large values of ${H}_{{\rm{T}}}=\sum | {p}_{{\rm{T}},j}| =350(500)\,\mathrm{GeV}$ for 8 (13) TeV, where the H_T sum runs over all jets with ${p}_{{\rm{T}},j}\gt 40\,\mathrm{GeV}$ and $| {\eta }_{j}| \lt 3.0$. The trigger for the 13 TeV analysis based on 2015 data additionally requires either two jets with ${p}_{{\rm{T}}}\gt 40$ GeV and no more than two associated prompt tracks (d₀ < 1 mm) and the H_T threshold is lowered to 350 GeV if the two jets each have at least one track that originates far from the PV¹⁵⁶ . Only events with two or more displaced jets are kept in the analysis, while those with only one are used as a control sample to estimate the prompt jet misidentification rate. For cτ < 3 mm¹⁵⁷ , the algorithm is inefficient as more than two tracks tend to have impact parameters less than 1 mm; for cτ > 1 m the search is inefficient as most decays occur too far from the PV to form reconstructable tracks. A key difference among these searches is that the 8 TeV [251] and 13 TeV (2016 data) [250] analyses explicitly reconstruct the DV, while the 13 TeV (2015 data) [249] analysis does not.

CMS interprets the signal in several benchmark models that can be mapped to the direct pair production simplified model production mode, including a neutral LLP decaying hadronically and a color-charged LLP decaying into a jet plus a lepton. For neutral LLP pair production decaying democratically into light jets, the trigger efficiencies for cτ = 30 mm are reported to be 2%, 41%, 81%, and 92% for 50, 100, 300, 1000 GeV masses, respectively. It is evident that the requirements on H_T and on ${p}_{{\rm{T}},j}$ make the search inefficient for low LLP masses. Indeed, a phenomenological recast of the 8 TeV analysis [251] in terms of rare decays of a SM-like Higgs boson with a mass of 125 GeV Higgs sets very mild bounds for LLP masses below m_h/2 [260]. Thus, the CMS search has limited sensitivity to low-mass, hadronically decaying LLPs through the Higgs, $Z^{\prime}$, or CC simplified production modes.

As mentioned above, CMS also has a search for DV in multijet events [252], which was released near the time of the final editing of this manuscript.

The LHCb searches [253, 254] trigger directly on DVs with a transverse distance of L_xy > 4 mm) with four or more tracks, vetoing dense material regions in which hadronic interactions with the detector can mimic LLP decays. The trigger thresholds are, however, low. For example, the invariant mass of particles associated with the vertex must exceed 2 GeV and the scalar sum ${p}_{{\rm{T}}}$ of tracks at the vertex must exceed 3 GeV. Jet reconstruction is then performed offline with standard algorithms. The benchmark model used by these searches is a scalar particle decaying to two neutral LLPs, ${\pi }_{{\text{}}v}$ (dark or 'valley' pions), which corresponds to the Higgs simplified model with hadronic decay modes. The parent particle can be either a SM-like 125 GeV Higgs [253] or a Higgs-like scalar with mass in the 80–140 GeV range [254]. The search is performed for ${\pi }_{{\text{}}v}$ masses between 25 and 50 GeV and decay lengths between 0.6 and 15 mm. It is expected that LHCb will extend their coverage to shorter lifetimes by improving the understanding of the material and to lower masses by using fat-jets and jet-substructure to access larger boosts [261]. In principle, the search is also sensitive to direct pair production of LLPs.

Because of the low thresholds, the LHCb search focuses on low-mass LLPs with short lifetimes, for which it has excellent sensitivity. However, its sensitivity for other signatures is limited by the geometry of the detector and the LHCb luminosity compared to ATLAS and CMS. A model-dependent direct comparison among the LHCb, ATLAS and CMS reaches for the Higgs production mode decaying into dark pion LLPs can be seen in figure 4.

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Searches in hadronic final states do not currently cover LLP parent masses below ∼100 GeV in a comprehensive way. This is typically due to the large ${p}_{{\rm{T}},j}$ requirements at the trigger level, with an exception being the DV reconstruction at LHCb. Additionally, the powerful ATLAS searches for LLPs decaying in the HCAL or MS require two LLP decays in the detector, meaning that as of this writing there is no sensitivity to singly produced long-lifetime LLPs with hadronic decays¹⁵⁸ . While the existing searches are typically sensitive to both direct pair production and HP production of LLPs, not all of the searches provide benchmarks with a variety of LLP production kinematics and boost.

A potential way to extend the sensitivity of current analyses is to use other existing triggers exploiting such things as VBF production modes, leptons, ${{/}\!\!\!\!{E}}_{{\rm{T}}}$, etc, to trigger on associated prompt objects and perform the hadronic DV reconstruction offline. The ATLAS 8 TeV study [196] does employ multiple triggers (such as lepton triggers), but in each case the triggered object must be associated with the DV (for a lepton trigger, the lepton must originate from the DV). If, instead, a prompt lepton or VBF trigger were used with the offline reconstruction of a separate displaced object, sensitivity could be recovered to low-mass hadronic DVs in a variety of simplified models, including Higgs production (via VBF or VH associated production modes) [260, 263] or CC production (in association with a prompt lepton) [264]. In particular, triggering on associated prompt objects would improve the efficiency of reconstructing low-mass hadronic LLPs produced in the decays of a SM-like 125 GeV Higgs. As there is no theoretical lower limit on the masses of light neutral LLPs, it is imperative to lower the LLP mass coverage as much as possible. If at all possible, a dedicated online reconstruction of DVs would allow for a further reduction on the ${p}_{{\rm{T}}}$ threshold, giving sensitivity to light LLP masses.

The CMS searches trigger on leptons reconstructed using information from either the tracker [265] or the muon chambers [266], where the latter search uses only muons. In the tracker-based analysis, the LLP is reconstructed by forming pairs of charged leptons (where muons are required to have opposite signs), with ${p}_{{\rm{T}}}$ cuts of 26 GeV for muons, and 36 (21) GeV for the leading (subleading) electron. This yields slightly larger efficiencies in the muon channel. The transverse impact parameter $| {d}_{0}|$ needs to be 12 times larger than its uncertainty σ_d (approximately corresponding to a distance ≳ 200 μm) to reject prompt backgrounds. In the MS-based analysis, muon candidates are reconstructed using hits in the muon chambers, and no information from the silicon tracker is used. In order to avoid biases from a loose beamspot constraint in the seeding step, these muons undergo an additional refit step. These candidates are referred to as re-fitted stand-alone muons, and they need to fulfill ${p}_{{\rm{T}}}$ > 26 GeV, $| \eta | \,\lt$ 2, and to be separated by ΔR > 0.2. More importantly, these candidates are rejected if they can be matched to a ${p}_{{\rm{T}}}$ > 10 GeV track in the inner tracker, which efficiently excludes prompt muons and also renders this study fully complementary to the tracker-based one. Both these searches are interpreted in terms of decays of an SM-like Higgs H ($H\to {XX},X\to {l}^{+}{l}^{-}$) and RPV squarks, covering proper lifetimes of 0.01–10⁵ cm for the Higgs scenario, and 0.1–10⁴ cm for the SUSY case. The difference in the lower reach of cτ is due to the larger boost factor of the Higgs. These benchmarks map to the direct pair production, HP and Higgs production simplified models, with flavor-conserving leptonic decays of the LLP. There is good sensitivity down to relatively low masses (LLPs of masses ≳ 20 GeV produced in Higgs decays) due to the low lepton trigger thresholds.

Additionally, CMS has a search for one electron and one muon, each with large transverse impact parameter (200 $\mu {\rm{m}}\lt | {d}_{0}| \lt 10\,\mathrm{cm}$) [197]. Events are selected using a dedicated trigger for eμ pairs that applies a ${p}_{{\rm{T}}}$ cut on the leptons (42 GeV for electrons, 40 GeV for muons) but, unlike standard triggers, places no restriction on the maximum d₀ or distance from the PV. Events with exactly one muon and exactly one electron are kept, and then separated into 'prompt', 'displaced control' and 'signal' regions, defined as $| {d}_{0}| \,\lt$ 100 μm, 100 $\mu {\rm{m}}\lt | {d}_{0}| \,\lt$ 200 μm, and $| {d}_{0}| \,\gt$ 200 μm, respectively. This selection makes the signal region almost free of leptons coming from SM processes, with rare tau-leptons, B-mesons or D-mesons as the largest remaining background.

Although in the original search the results are interpreted in the context of long-lived RPV stops (excluding masses below 870 GeV for cτ = 2 cm)¹⁵⁹ , this search has been shown to be sensitive to many scenarios, including long-lived staus in gauge mediated SUSY breaking [205] and RHNs [45]. Indeed, this search has sensitivity to LLPs produced via any of the simplified model production modes and (semi)-leptonic decays that give exactly one electron and one muon. On the other hand, models where LLPs decay only to either muons or electrons (e.g. $\tilde{\mu }\to \mu \tilde{G}$) are unconstrained by this search. Furthermore, same-sign lepton signatures and signatures with additional leptons are not constrained by the current search but could be covered by extensions of the search [45, 205]. Due to the generality of tau-specific models, searches for hadronic tau channels is also desirable. This search has sensitivity to relatively low-mass LLPs; however, the 8 TeV analysis [275] has lower thresholds (${p}_{{\rm{T}}}$ > 22 GeV on both leptons) albeit with a requirement for shorter decay distances ($| {d}_{0}| \,\lt$ 2 cm), and so has superior sensitivity to very low-${p}_{{\rm{T}}}$ displaced signals. Maintaining low trigger thresholds is necessary to obtain sensitivity to the lowest-mass leptonic LLP signals.

The primary ATLAS search for displaced leptons [196] triggers on muons without an ID track, electrons, or photons¹⁶⁰ . The trigger and offline ${p}_{{\rm{T}}}$ criteria are relatively high, requiring one of the following: one muon of at least 50 GeV; one electron of at least 110 GeV; one photon of at least 130 GeV; or two electrons, photons, or an electron and a photon with minimum ${p}_{{\rm{T}}}$ requirements for both objects in the 38–48 GeV range. The DV is formed from opposite-sign leptons, irrespective of flavor, and needs to be located more than 4 mm away from the PV in the transverse plane. DVs in regions with dense detector material are vetoed to suppression backgrounds from converted photons (e.g. $\gamma p\to {e}^{+}{e}^{-}p$). This search is in principle sensitive to events with a reconstructed DV mass m_DV > 10 GeV, but the high ${p}_{{\rm{T}}}$ requirements for the leptons restrict the sensitivity to low-mass LLPs.

ATLAS has also recently released a search for pairs of muons that correspond to a DV [276]. This search is sensitive to LLP decays that occur sufficiently far from the IP that the muons are reconstructed only in the MS. The analysis has four separate trigger pathways: ${{/}\!\!\!\!{E}}_{{\rm{T}}}\gt 110\,\mathrm{GeV};$ one muon with ${p}_{{\rm{T}}}$ > 60 GeV and $| \eta | \lt 1.05;$ two muons with ${p}_{{\rm{T}}}\gtrsim 15\,\mathrm{GeV}$ and ${\rm{\Delta }}{R}_{\mu \mu }\lt 0.5;$ or three muons with ${p}_{{\rm{T}}}\gt 6\,\mathrm{GeV}$. Thus, the search has sensitivity to final states with high and low masses (down to m_μμ = 15 GeV), as well as with various lepton multiplicities. Offline selections require the muons to have ${p}_{{\rm{T}}}\gt 10\,\mathrm{GeV}$ and opposite charge, and the search is efficient at reconstructing muons for transverse impact parameters up to $| {d}_{0}| =200\,\mathrm{cm}$. Muons are also required to satisfy isolation requirements from jets as well as from nearby tracks. The search puts constraints on a SUSY model and a model of dark photon production in Higgs decays; this can be used to determine sensitivity to all of the simplified production modes from chapter 2 in the μμ decay mode (or μμ in association with other objects). It also demonstrates how combining many trigger pathways and loose selection requirements can enhance sensitivity to a wide range of LLP models.

LHCb has a search that looks for the direct production of both promptly decaying and long-lived dark photons [269]. As a result of the direct production, dark photons do not tend to be highly boosted in the transverse direction. Events¹⁶¹ are required to have a single muon with ${p}_{{\rm{T}}}$ > 1.8 GeV, or two muons with a product of transverse momenta ≳ (1.5 GeV)². The displaced search constrains previously uncovered dark photon parameter space around masses of ∼300 MeV.

The LHCb searches for displaced leptons in rare B meson decays [267, 268] rely on standard techniques to identify the B^±decay vertex and the kaons and pions in the event, and the di-muon invariant mass $m({\mu }^{+}{\mu }^{-})$ variable is scanned for excesses. The $X\to {\mu }^{+}{\mu }^{-}$ vertex is not required to be displaced from the ${B}^{\pm }$ vertex, and thus the constraints apply to both prompt and LLPs. The analysis probes LLP masses of 214 (250) MeV < m_X < 4350 (4700) MeV for the ${B}^{0}\to {K}^{* }{\mu }^{+}{\mu }^{-}$ (${B}^{+}\to {K}^{+}X,X\to {\mu }^{+}{\mu }^{-}$) process, with the mass range being limited by kinematics.

Searches for LJs are focused on ${ \mathcal O }(\mathrm{GeV})$ LLP masses and distinctly boosted signatures, and thus we treat them separately.

The ATLAS 8 TeV search [272] considers three types of LJs: those containing only muons, only electrons/pions, or a mixture of the two. The muon and electron/pion LJs can contain either two or four leptons, while the mixed LJ must contain two muons and a jet consistent with a displaced electron/pion pair. As these signatures contain relatively soft leptons, the ATLAS 8 TeV analysis uses a trigger that requires three muon tracks in the MS with ${p}_{{\rm{T}}}\gt 6\,\mathrm{GeV}$. There is a built-in limitation to this trigger, which is that the L1 requirement of three separate muon RoIs makes it only sensitive to topologies with two LJs in which one LJ has a wide enough opening angle between two muons to create two level-one RoIs. For the electron LJs, when the electrons are produced in the HCAL they are indistinguishable from a hadronic decay and thus the CalRatio trigger is used.

In the 13 TeV ATLAS analysis [273], a narrow-scan muon trigger is additionally used. This trigger starts off by selecting events with one muon with ${p}_{{\rm{T}}}$ > 20 GeV, then requires a second muon with ${p}_{{\rm{T}}}$ > 6 GeV within ΔR = 0.5 of the leading muon.

Both the 8 and 13 TeV ATLAS searches are interpreted for Higgs-like scalar particles (with masses of 125 and 800 GeV) that decay effectively into either two or four lepton pairs, with each lepton pair assumed to come from a low-mass 'dark' photon, γ_D. The ATLAS result excludes exotic Higgs branching ratios below 10% for dark photon lifetimes 2 < cτ < 100 mm. Note that here γ_D is also allowed to decay to pions and so the results can also be interpreted for hadronically and semi-leptonically decaying LLPs. This corresponds to the Higgs production mode in the simplified models proposal with an admixture of flavor-conserving leptonic and hadronic LLP decays.

The CMS LJ search focuses on fully muonic LJs and has been performed with both the 8 TeV dataset [270] and part of the 13 TeV dataset [271]. The 13 TeV search is sensitive to di-muon parent particle masses up to 8.5 GeV. Events are selected with a di-muon trigger with standard isolation requirements. Further selection requires at least four muons, forming a minimum of two opposite-charged pairs. CMS uses a benchmark model with scalars decaying into either lighter scalars or dark photons, with varying scalar and dark photon mass. For the case of a 125 GeV Higgs they can exclude an exotic branching ratio of below 0.1% for some parameter points. The CMS search can be compared with the ATLAS results, as can be seen in figure 5. We note that this study includes sensitivity to both prompt and displaced muonic lepton jets.

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To summarize, the lepton searches rely on fairly standard lepton identification, with vertex reconstruction being performed mostly offline. Searches for leptonically decaying LLPs typically enjoy low trigger thresholds and good sensitivity to LLP production rates. Extending the success of the leptonic LLP program to future LHC running will necessitate maintaining low-threshold triggers for displaced leptons in a high-luminosity environment; this is a major challenge but one that must be overcome. Another outstanding challenge is coverage of LLP decays to τ leptons, which lie at the interface between hadronic and leptonic searches. Such decays are very well motivated from the theoretical point of view, as a Higgs-like scalar can typically decay about 300 times more often into ${\tau }^{+}{\tau }^{-}$ if kinematically allowed, and also one could have large rates into mixed decay modes such as ${\tau }^{+}{\mu }^{-}$. A displaced hadronic τ is a striking object, and most likely will have few backgrounds. Hence, limits on exclusive displaced τs would be of utmost importance¹⁶² .

As the leptonic searches explicitly require opposite-sign leptons, the same-sign lepton signature (motivated from Majorana neutrinos; see the LHCb search in section 3.3, or heavy, doubly-charged LLPs) is currently neglected. Furthermore, the sensitivity of the CMS search for two high-$| {d}_{0}|$ leptons is currently only sensitive to opposite sign eμ pairs, with a veto on additional leptons. Relaxing these requirements would greatly enhance sensitivity to certain scenarios, especially the simplified models with flavor-conserving leptonic LLP decays.

Lepton-jet searches currently cover only final states with at least two LLPs and some muons in the final state¹⁶³ , and the same statement currently applies to both the LHCb searches for dark photons [269, 277] and for LLPs produced in B-meson decays. The existing ATLAS LJ studies express their results in terms of specific dark photon models¹⁶⁴ , which makes it complicated to apply the results to other models. We refer the reader to section 6 for a further discussion of this topic. In extending LJ searches, it would be beneficial to have additional searches with a single LJ or low-mass, leptonically-decaying LLP (which are motivated in models with hidden sectors and Majorana neutrinos, for example in [43, 135]). In addition, the status of coverage in the intermediate mass-transition region between 'standard' displaced lepton pairs and LJs is unclear, and may potentially harbor a gap; adopting the simplified model approach for leptonic LLP decays with masses varying between the GeV and weak scale would ensure comprehensive coverage of low-mass leptonically decaying LLPs.

Finally, we comment on gaps in sensitivity to very low-mass leptonically decaying LLPs. A benchmark LLP model is the heavy neutral lepton (HNL), which corresponds to the CC production mode with (semi-)leptonic LLP decays in our simplified model framework. HNLs constitute an important physics case that leads to multi-lepton displaced signatures from W decays, with nice prospects at ATLAS and CMS (see, e.g. [43, 48, 49]). While previous searches were not sensitive to this scenario due to either high-${p}_{{\rm{T}}}$ requirements or the requirement of two DVs in the same event, the presence of a prompt lepton from the W allows the relaxation of these requirements in a dedicated analysis. Moreover, the prospects of triggering on a prompt lepton in such searches was studied recently in [48] and demonstrated in a prompt search in [278] ¹⁶⁵ . The identification of two leptons from the vertex is a powerful discriminant against backgrounds from meta-stable particle decays and hadronic interactions in material. This permits a potentially cleaner exploration of the lower HNL mass range (3–6 GeV) than in the semi-leptonic channel (see section 3.3) despite the lower branching ratio. It should be noted that HNL models can predict LLP decays to all three lepton flavors (either democratically or hierarchically), necessitating the capability to reconstruct displaced leptons of all flavors, including taus.

The LHCb search for semi-leptonic LLP decays selects events with a muon trigger, then reconstructs a DV offline [279]. The results are interpreted in terms of four distinctive topologies: single LLP production in association with a new particle (in this case a gluino), double LLP pair production via direct pair production, Higgs decay, or via squark pair production (HP). The LLP then decays to two quarks and a muon (which maps to the ${jj}{\ell }$ simplified model decay). Material regions are vetoed for the DV, which results in the dominant background arising from heavy flavor production either directly or from W/Z decays. The signal discrimination is obtained from a multivariate analysis based on the muon ${p}_{{\rm{T}}}$ and impact parameter, and subsequently the search is optimized based on the LLP reconstructed mass and the muon isolation. This study is sensitive to low-mass LLPs with lifetimes between 1.5 and 30 mm, as can be seen in figure 6.

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The LHCb search for Majorana neutrinos [280], N, probes Majorana neutrinos produced in leptonic B decays, ${B}^{\pm }\to {\mu }^{\pm }N$. The Majorana neutrino subsequently decays exclusively to $N\to {\mu }^{\pm }{\pi }^{\mp };$ both prompt and displaced decays are considered¹⁶⁷ . A same-sign muon requirement, along with the reconstruction of the N and B meson masses, greatly reduces backgrounds to the search. The sensitivity of the search is limited by the restriction to muons in the final state (so models that predominantly decay to e or τ are not constrained), and the same-sign lepton requirement gives sensitivity only to lepton-number-violating processes. More inclusive searches looking for additional N production modes [282], decays with opposite-sign leptons, or searches targeting decays of heavier mesons like B_c [283] could also improve the sensitivity to semi-leptonically decaying LLPs.

The ATLAS search for semi-leptonic LLP decays [196] looks for a vertex with a lepton accompanied by tracks. This search uses the same trigger as the dilepton vertex search described in section 3.2. The DV is required to have a lepton as well as at least four additional associated displaced tracks, and the invariant mass of the tracks must exceed 10 GeV. Thus, the search in principle can have sensitivity down to masses ≳ 10 GeV, although the high ${p}_{{\rm{T}}}$ threshold for the displaced electron/muon typically limits sensitivity to low-mass LLPs; the vertex must contain a muon with ${p}_{{\rm{T}}}$ > 55 GeV or an electron with ${p}_{{\rm{T}}}$ > 125 GeV.

When considering the application of inclusive hadronic or leptonic searches to semi-leptonic LLP decays, it is important to understand how the simultaneous presence of leptons and jets in the signal can degrade the sensitivity. For instance, prompt jet searches explicitly can remove non-standard jets through jet cleaning cuts. Lepton isolation criteria can severely reduce the signal acceptance for a highly-boosted LLP decaying into a lepton and a jet, and they might also veto extra tracks in the events. Thus, boosted semi-leptonic decays (as might be found in the displaced decay of a low-mass, RHN produced via W decay) may not be covered by existing searches.

One of the major gaps in semi-leptonic LLP searches is at the smallest LLP masses. In this case, it can be challenging for the leptons from LLP decays to pass trigger thresholds and/or isolation criteria; backgrounds from heavy-flavor and other processes are also higher for semi-leptonic processes than fully leptonic ones. However, there are very good motivations for low-mass semi-leptonic LLPs from the HNL benchmark model¹⁸ introduced in section 3.2.5, which predicts LLPs for HNLs of masses below 30 GeV. The signature of HNLs from W decays with displaced semi-leptonic HNL decays is an important item on the search agenda of ATLAS, CMS and LHCb [38, 43, 48, 49, 284, 285]. Recently, there has also been a proposal to search for low-mass HNLs in heavy ion collisions [286]. The semi-leptonic channel has the highest branching ratio (about 50% in the relevant mass range [287]) and can therefore offer the best discovery prospects at LHC experiments for HNL masses up to 30 GeV as long as a DV mass cut of around 6 GeV is made to mitigate backgrounds from B-mesons, m_B ∼ 5 GeV, and backgrounds from random-crossings can be suppressed. The lower end of the 6–30 GeV mass range corresponds to a non-perturbative regime for the hadronization of the HNL decay products. As the number of charged hadrons significantly affects the DV reconstruction efficiency, the validation of event generator outputs for this process is an important issue currently being addressed by the community (see e.g. [48]). The ability of LHCb to trigger directly on the HNL decay products and better reconstruct displaced tracks can in some cases compensate for its lower acceptance and luminosity, as exemplified by a recent search for DVs composed of one muon and several tracks [279, 285]; similar arguments can be made in the case of heavy ion collisions [286]. This possibly enables LHCb to better probe the more challenging tau channel. Figure 7 shows the overall expected reach of LHC searches in the HNL coupling strength (for the muon channel) versus mass plane, using assumptions detailed in [284], similar to those in [38, 43].

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The sensitivity of LHC experiments to HNLs is complementary to that of fixed-target experiments which can probe lower couplings thanks to high-intensity beams albeit at lower mass ranges (i.e. targeting HNLs from c and b decays). The CERN SPS provides great opportunities with the running NA62 experiment [296] and the planned SHiP experiment [289], which comprise a vacuum decay vessel and spectrometer tracker downstream of the target to reconstruct vertices of long-lived neutral particles¹⁶⁹ . These provide the best sensitivity to HNL masses up to 2 GeV, where they probe a region of the parameter space favored in models which simultaneously explain neutrino masses, matter–antimatter asymmetry and DM [295, 298–300] (see figure 7).

The ATLAS study [301] benefits from the capability of the liquid-argon electromagnetic calorimeters (ECALs) to measure the flight direction and the photons' TOF. Resolutions on Δz_γ, the separation between the PV of the event and the extrapolated origin of the photon, and $| {\rm{\Delta }}{t}_{\gamma }|$, difference of the arrival time of the photon with respect to the prompt case, are as low as 15 mm and 0.25 ns, respectively. The trigger demands two photons within $| \eta | \,\lt$ 2.5, with transverse energies ${E}_{{\rm{T}}}$ of 35 and 25 GeV. In addition, to guarantee the event comes from a proton–proton collision, a PV with five or more tracks with ${p}_{{\rm{T}}}$ > 0.4 GeV is required. The offline selection requires two photons with ${E}_{{\rm{T}}}$ > 50 GeV and $| \eta | \,\lt$ 2.3, not in the barrel-endcap transition region (1.37 < $| \eta |$ < 1.52), at least one of them in the barrel ($| \eta | \,\lt$ 1.37) and with less than 4 GeV of energy deposited in the calorimeter in a cone of ΔR = 0.4 around them (consituting the isolation criterion). In addition, the events are binned in ${{/}\!\!\!\!{E}}_{{\rm{T}}}$: the ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ < 20 GeV bin contains the prompt backgrounds, the 25 GeV < ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ < 75 GeV bin is used as the control region, and finally the signal analysis is performed in the ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ > 75 GeV bin. This study covers lifetimes from 0.25 to 100 ns in the GMSB framework, the lower limit being a hard cut-off imposed experimentally, as the similarity between background and signal samples in that region makes discrimination rather difficult. The excluded signal rates in this range of lifetimes vary between 0.8 and 150 fb, with the best-constrained value obtained for τ ∼ 2 ns.

The CMS study of delayed photons [303] follows a similar approach to ATLAS. The main difference is that it demands only one photon with ${p}_{{\rm{T}}}$ > 80 GeV, but in addition two jets are required. Furthermore, the vector sum of ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ and ${E}_{{\rm{T}}}^{\gamma }$, which is denoted ${{/}\!\!\!\!{E}}_{{\rm{T}}\mathrm{no}\gamma }$, is additionally used for background discrimination. Collisional backgrounds have small ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ and large ${{/}\!\!\!\!{E}}_{{\rm{T}}\mathrm{no}\gamma }$, while the non-collisional backgrounds are characterised by large ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ and small ${{/}\!\!\!\!{E}}_{T\mathrm{no}\gamma }$. For the signal events the two variables are large, hence they are both requested to be larger than 60 GeV. The time resolution is 0.372 ns, slightly worse than in the optimal scenario of the ATLAS search. Their reach in lifetimes lies in the 2–30 ns range, excluding signal rates of 10–30 fb.

The CMS study of non-pointing photons [304] relies on the photon converting to ${e}^{+}{e}^{-}$ pairs. It requires two photons, two additional jets, and ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ > 60 GeV. The photon trajectory is obtained from the conversion vertex as the line segment along the momenta of the ${e}^{+}{e}^{-}$ track pair, and the impact parameter, $| {d}_{{XY}}|$, is defined as the closest distance between the photon and the beam axis, which can be determined within approximately 1 mm. A comparison of the reach of these 8 TeV studies, as well as those using the 7 TeV dataset, can be found in figure 8.

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The gaps in these studies are straightforward to identify. The requirement of large ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ is due to the fact that all of these studies have an underlying theoretical picture of neutralinos decaying into gravitinos and photons, motivated from GMSB scenarios. Hence, these searches do not cover cases without the presence of missing energy, including LLPs that decay to γγ, lγ or jγ. It may be possible to extract a constraint on such LLP decay modes due to mis-measurement of jets or the photon decay geometry which could mimic large missing energy; however, this would be sub-optimal compared to a dedicated search. With the exception of the CMS study [303] which requires two additional hard jets, all of these analyses require two displaced photons. A single displaced photon signature can occur in motivated models: it can easily arise, for example, from a very slightly mixed electroweak triplet and singlet as in SUSY theories (see the UV models in section 2). Furthermore, as discussed in section 3.1, a single LLP in the detector can also arise for very large lifetimes of neutral LLPs, which limits the reach of current searches at longer lifetimes. In such scenarios, it is possible that the photons from LLP decay can be quite soft, and obtaining sensitivity to models with single photons from LLP decay and/or low momenta may require triggering on associated prompt objects, similar to the recommendations in section 3.1.4.

In this category, we collect all searches for charged-particle tracks with anomalous ionization, i.e. those that are inconsistent with a charge $| Q| =e$. Here we include (i) the so-called HSCPs, which apply to stable, electrically charged particles but also charged particles that decay in the calorimeters and/or MS; and (ii) magnetic monopoles.

3.5.1.1. Heavy stable charged particles

3.5.1.2. Magnetic monopoles

ATLAS [215] has a dedicated search for highly ionizing particles (HIPs), which encompass a variety of new physics scenarios, such as magnetic monopoles, dyons (particles with both magnetic and electric charge), stable microscopic black holes, etc. For the sake of concreteness, we focus on magnetic monopoles but the interpretation in terms of other models is straightforward¹⁷² .

The main phenomenological feature is that magnetic charge is quantized in units of g_D = 2π/e ≈ 68.5. Hence, a magnetic monopole behaves as a particle with at least 68.5 electron charges, leading to an unusually large ionization power in matter, so that they would quickly stop in the detector because HIPs lose energy at spectacular rates. Because of the large QED coupling of magnetic monopoles, a perturbative calculation of the cross section is invalid and there is no accurate determination of the production rate, but a naïve Drell–Yan production cross section is provided for the purposes of comparison. The specifics of the detector restrict the sensitivity of this search to magnetic charges g < 2g_D because a large fraction of the monopoles stop in the material upstream of the ECAL, as the latter is used for the L1 trigger [310]. We note that larger magnetic charges can be tested by the MoEDAL experiment [311], which is described in detail in section 5.3.2. Additionally, theories with monopoles can also be tested in heavy ion collisions [312].

ATLAS [215] has a dedicated trigger for HIPs based on identifying relevant RoIs in the ECAL and subsequently counting the number of hits in the TRT. As well, the fraction of TRT hits that are high-threshold (HT), meaning that they have an ionization larger than ∼3 times that expected from a SM particle, is used as a discriminant. The analysis selects events based on the fraction of TRT-HT hits matched to an EM cluster deposit, and how the energy deposits are distributed in the different layers of the ECAL. It is important to note that due to the lack of a consistent theory, the signal simulation is performed by re-scaling Drell–Yan production at leading order and assuming no coupling to the Z boson. The HIPs are assumed to have either spin-0 or 1/2. The spin does not affect the interaction with the material, but the angular distributions are different according to angular momentum conservation (keeping in mind that there is, of course, no perturbative theoretical prediction for the angular distribution). Cross section limits for 0.5 < $| g| /{g}_{D}$ < 2 are set for masses in the 890–1050 (1180–1340) GeV range for the spin-0 (1/2) case.

The coverage in LHC Run 2 of magnetic monopoles in the ${g}_{D}\mbox{--}\sigma$ plane is displayed in figure 9.

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In this category we group searches where the tracks have an anomalous geometry, namely they disappear (track →  nothing), or follow non-standard trajectories (such as quirks). There are additional anomalous track signatures that we do not cover such as kinked tracks, where a charged LLP decays to another charged particle that travels at a non-zero angle with respect to the LLP direction [112, 313–315]; however, there are currently no dedicated searches for such signatures.

Within this category we also have the emerging jets signature that has been recently studied by CMS [316]. Since emerging jets arise from dark sector radiation, they are described in detail in chapter 7 in conjunction with the theoretical and phenomenological aspects of dark showers.

3.5.2.1. Disappearing tracks

Massive charged particles traveling in the detector can decay to a lighter, almost mass-degenerate neutral state, emitting a soft SM charged particle (typically a pion or a muon). While at first glance a small mass gap naïvely seems like a hallmark of tuning, near degeneracies often occur naturally as a result of a symmetry. In fact, electroweak symmetry generically leads to small mass splittings between components of a single electroweak multiplet. For example, ${ \mathcal O }$ (100 MeV) splittings arise between the different components of an electroweak multiplet [64, 128] due to EW gauge boson loops¹⁷³ . If the SM particle is sufficiently soft it cannot be reconstructed, and then a charged track seems to vanish: this is thus referred to as a DT¹⁷⁴ . The actual lifetime of the charged particle is highly sensitive to the precise value of the mass splitting. For instance, the well studied cases of a fermionic doublet with Y = 1/2 and a fermionic triplet with Y = 0, reminiscent of a Higgsino and Wino in supersymmetry, respectively, have mass splittings of Δ = 355 and 166 MeV, up to small corrections, but the corresponding cτ values differ by almost an order of magnitude: 6.6 mm versus 5.5 cm¹⁷⁵ .This is because the lifetime, cτ, depends on the third power of the mass splitting in these scenarios when the charged LLP decays to a charged pion [64, 128].

Before 2017, both ATLAS [317] and CMS [217] required a track to travel about 30 cm in order to be reconstructed, giving good coverage of the Wino scenario. This 30 cm value corresponds to four hits at ATLAS, three in the pixel layers plus one in the silicon tracker, and to seven hits in the pixel and trackers of CMS. The search employs a trigger requiring an ISR jet against which the charged particle recoils, along with the presence of large ${{/}\!\!\!\!{E}}_{{\rm{T}}}$. The DT is reconstructed offline and needs to fulfill quality criteria (isolation, ${p}_{{\rm{T}}}$ threshold, etc). A phenomenological study [99] has shown that reducing the distance from 30 to 10 cm would give coverage to the elusive Higgsino scenario, moving the expected reach up to 400 GeV, surpassing the expected mono-jet reach of 250 GeV [318–320]. Later, ATLAS presented a study [218, 321] using 13 TeV data and exploiting the presence of a new innermost pixel layer (IBL). This addition allows for all four hits to be in the pixel, with the outermost pixel layer now at 12.25 cm, enhancing sensitivity to lower values of cτ. The summary for DTs at ATLAS for the Wino case can be seen in the left panel of figure 10, while in the right panel we show the constraints for Higgsinos from [99]. CMS also has a DTs search using 2015 and 2016 data at a center-of-mass energy of 13 TeV [322].

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At LHCb the prospects for a DT analysis with the present detector are poor. Currently, the momentum of the track can only be measured if the particle passes through the tracking station (TT), which is about 3 m away from the IP. Particles decaying in the vertex locator (VELO) or RICH1 system will not leave a fully-measurable track and will be swamped in a background of SM processes such as kaon decays, which would give a similar signature in the detector components before the magnet. Detector improvements (additional magnets, better PID at low momentum, additional layers) might lead to some sensitivity for ${ \mathcal O }$(cm) lived tracks, a golden opportunity for potential LLP discoveries at LHCb in the HL-LHC era.

To summarize, the search for DTs presents a few challenges. Using an ISR jet trigger means a price is paid in terms of signal efficiency. For example, [99] has shown that significantly lowering the ${p}_{{\rm{T}}}$ threshold of the jet or directly triggering on the momentum of the DT¹⁷⁶ would lead to a factor of two increase in the number of signal events. It is also clear that better access to lower lifetimes is needed; this may only be possible, for instance, by adding new tracking layers as close as possible to the beampipe (and/or having double layers instead of single ones).

3.5.2.2. Strongly interacting massive particles

SIMPs can be motivated by astrophysical observations of DM that do not fully agree with the WIMP paradigm (e.g. missing satellites, the core versus cusp problem; see, e.g. [327–330] for further discussion). These particles are assumed to interact strongly with baryons. Consequently, the experimental signature is little to no signal in the tracker and the ECAL, and large energy deposits in the HCAL. Such a final state with trackless jets also arises in the context of emerging jets [331], and ATLAS has a trigger for trackless jets in association with a soft muon (where the muon is required to fire L1 of the trigger) [256]. Additionally, the CalRatio trigger and associated search for displaced hadronic decays (addressed in section 3.1) is designed to be sensitive to a similar signature and could provide some coverage of this signature as well. Strictly speaking, SIMPs are not a track-based signature, but we include them here because the interactions of the SIMPs with the tracker are different from usual hadrons in jets, while the calorimeter signatures are similar.

An LHC phenomenological study of SIMPs was carried out in [332]. We summarize the main points of the study here. In their setup, SIMPs interact with the SM via an attractive potential (either scalar or vector mediator) coupling SIMP pairs to $q\bar{q}$ pairs. The proposed analysis selects events with high-${p}_{{\rm{T}}}$, back-to-back jets within the tracker, exploiting the charged energy fraction within a jet to discriminate signal from background. The astrophysical experimental constraints on this scenario are compared with the expected reach of this search and that of mono-jets in figure 11. Currently there is an ongoing analysis in CMS pursuing this strategy.

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3.5.2.3. Quirks

This category is unique because LLP decays occur out-of-time with the collision. Indeed, decays can even occur when the LHC is not running! The only member of this class is the search for SPs, which we describe below.

If an HSCP is produced with very low kinetic energy, it can come to rest in the detector due to interactions with the detector materials. This most likely occurs in the calorimeters or the steel yoke in the MS as a result of their high material densities. The HSCP can then decay at a later time when no collision is taking place (known as an out-of-time decay). This experimental restriction reduces the types of background processes affecting the search, with the dominant backgrounds coming from cosmic rays (CRs), beam halo, and instrumental noise.

In the Run 1 analyses from ATLAS [236] and CMS [234], events are selected with a dedicated trigger selecting bunch crossings which are empty and have no bunches of protons nearby. The analyses require a jet with ${p}_{{\rm{T}}}$ (E) above 30 (50) GeV at ATLAS (CMS). ATLAS further supplements the hardware trigger by requiring ${p}_{{\rm{T}}}$(j) > 50 GeV, $| \eta | \,\lt$ 1.3 and ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ > 50 GeV, rejecting instrumental noise. In addition, CMS has updated the jet search in Run 2 and also provided a search that triggers on out-of-time muons, both of which use the 13 TeV dataset [235]. The latter also employs the displaced stand-alone (DSA) muon reconstruction algorithm [335].

An offline selection procedure is aimed at reducing the main backgrounds. Muons coming from CRs can be identified due to their distinctive topology. The 'beam halo' background is the result of protons interacting with residual gas in the beampipe, the beampipe itself, or collimators upstream from the IP. Most particles will not travel far before being absorbed by various structures, but muons will travel parallel to the beam and can leave calorimeter deposits out of time with a proton–proton collision. However, these deposits will often be accompanied by corresponding horizontal tracks in the MSs and can thus be efficiently vetoed. Instrumental noise is rejected in CMS by exploiting the anomalous response in the HCAL.

Stopped particle searches provide an alternative way of probing charged particles besides more conventional HSCP searches. HSCP searches are typically more sensitive to any signature with a charged particle, so SP searches are not often expected to be a discovery mode for most simple new physics scenarios with charged LLPs¹⁷⁷ . The typical added value of SP searches is that they can help identify and characterise positive signals in HSCPs, for instance by providing a cleaner extraction of the lifetime and also to properly identify the decay products. However, in some cases (such as for quirks, where HSCP searches are insensitive in much of parameter space), it has been argued that an SP search could actually be a discovery mode if modifications are made to the search strategy to improve sensitivity to quirks [334]. These modifications that would increase quirk acceptance or lower backgrounds include expanding the η range, implementing higher energy thresholds, using the timing information, and considering shower evolution in the new CMS endcap calorimeter [336].

Cosmic rays from the atmosphere can enter the detector as cosmic-ray muons. These cosmic-ray muons can be reconstructed as displaced muons in the MS or as displaced jets in the calorimeters. If cosmic-ray muons are reconstructed in the MSs, they will typically appear as two back-to-back muons with ϕ values near ±π/2. The rate of cosmic muons in the detector is about 500 Hz at L1, but depending on the HLT path and the offline selection used, the rate of cosmic-ray muons entering a given LLP analysis is generally much less.

Cosmic-ray muons are typically an important background source to consider for displaced signatures, especially those with large displacements [234, 236, 343–345]. Cosmic-ray muons are generally only an issue for LLP analyses in CMS and ATLAS since LHCb has coverage only in the forward direction.

For many analyses, cosmic-ray muons can be rejected with a simple veto on back-to-back dimuons. However, in some LLP analyses, this veto is not optimal for the signal acceptance or it is insufficient to suppress cosmic-ray backgrounds. Another often-used way to minimize the contribution from cosmic-ray muons is requiring high-momentum muons and/or high-energy jets, since cosmic-ray muons have a rapidly falling ${p}_{{\rm{T}}}$ spectrum. In addition, if a search primarily looks for inner-tracker or calorimeter objects, cosmic-ray-muon events can be rejected by requiring little MS activity [234, 343, 344].

If the cosmic-ray muon background is significant for an analysis, it can be estimated using data from dedicated cosmic data-taking runs or from empty bunches in pp collision runs [234, 343, 344]. Cosmic ray muon simulations can be made, but in many LLP analyses, a data-driven approach is favoured if the simulation modeling is found to be insufficent. Timing information in the calorimeters or the MSs can be used to discriminate the signal from cosmic-ray muons, sometimes in conjunction with impact parameter variables.

Another type of real particle generated outside the detector that could be a significant source of background for LLP searches is beam halo. Beam halo is produced when protons from the LHC beam scatter off the LHC collimators and produce debris, which can appear in the detector. Beam halo can create energy deposits in the calorimeters or hits in the MS, both of which would be largely in the beam direction. These energy deposits or MS hits would appear earlier than if they had been made from particles coming from the collision (see figure 15). Beam halo is usually not modelled in MC simulation, since it is highly dependent on the beam parameters.

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Beam halo is most relevant for searches for displaced signatures without tracks in the inner tracker and for searches for decays in non-collision bunches (e.g. from SPs) [234, 343, 344], which are described in section 3.5.

The contribution from beam halo can often be reduced by requiring high-momentum or high-energy reconstructed objects. One can also decrease the number of beam halo events by requiring central objects or vetoing forward MS activity, since beam halo is usually in the very forward direction [234, 343, 344]. For inner tracker-based signatures, events from beam halo are rejected by requiring a minimum number of early hits; in this way beam halo is rejected due to its anomalous timing.

Beam halo background can be estimated using data control regions near ϕ = 0 and π. One could also identify cells with a low number of (or zero) tracks that are assigned an early time.

Diffuse backgrounds can also arise from proton–proton collisions filling the LHC caverns, consisting mostly of neutral, low-energy, and long-lived SM particles (i.e. neutrons and photons), leading to an overall increase in occupancy, especially in the MSs. This so-called 'cavern background' or 'cavern radiation' can constitute a significant background in a LLP search. As simulations are resource-intensive, it is usually not at all modelled in MC simulation samples.

Cavern radiation is most relevant for searches looking in non-collision data, that is, stopped-particle searches, and for searches using MS information to form tracks and vertices. It can be estimated from data by collecting events triggered by random triggers when there are no collisions, as was done in [236] ¹⁷⁸ . Cavern radiation can also be estimated by overlaying a cavern radiation simulation with minimum-bias events from data.

This type of background, illustrated in figure 16, is especially important in the environment close to the interaction region that experiences a high track density, and arises from two main sources. First, two or more individual tracks can cross each other and can be reconstructed as a DV. Second, two close-by, low-mass vertices can be reconstructed as one high-mass DV; such a final merging/cleaning step is often part of vertexing algorithms to reduce fakes in standard vertexing.

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The former source is mostly suppressed by requirements originally targeting the removal of meta-stable SM particles: a minimum transverse impact parameter, $| {d}_{0}|$, for tracks and a minimum distance between the PV and a given DV.

The latter source is harder to suppress, though can be estimated by randomly merging vertices from distinct events. By studying the number of reconstructed 'merged' high-mass vertices as a function of distance between the two low-multiplicity low-mass vertices that were 'merged'—both with vertices from the same event, as well as from different events and scaling them accordingly—an estimate for this background can be derived. This method has been successfully used in the ATLAS search for DV [237] and the ATLAS multitrack analysis [196].

A background that is typically more relevant than merged vertices is the background stemming from low-mass DV crossed by unrelated tracks, resulting in the reconstruction of a high-mass vertex, as illustrated in figure 17. The mass of the reconstructed DV is especially increased when the random track crosses the vertex in a direction that is perpendicular to the distance vector pointing from the PV to the displaced one.

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As demonstrated in detail in [196, 237], this background can be estimated by constructing vertices (n-track) from lower-multiplicity ones ($n-1$-track) by adding pseudo-tracks, drawn randomly from data-driven track templates derived for various radial detector regions. The normalization of the prediction is performed by comparing the $n-1$-track-based constructed vertices with the actual n-track vertices in all radial detector regions. One potential method for suppressing such backgrounds is to veto vertices where removing one track substantially decreases the mass of tracks associated with the vertex.

The high luminosity LHC (HL-LHC) will begin with the third long shutdown (LS3) of the LHC in the coming decade (as of this writing estimated to begin at the end of 2023), where the machine and detectors will be upgraded to allow for pp running at a luminosity of $5\times {10}^{34}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ in the nominal scenario, or potentially $7.5\times {10}^{34}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ in the ultimate performance scenario. This will allow the ATLAS and CMS experiments to collect integrated luminosities ten times that of the current operations, which amounts to around 300 fb⁻¹ per year and 3000 fb⁻¹ during the projected HL-LHC lifetime of ten years (up to 4000 fb⁻¹if the ultimate instantaneous luminosity can be achieved).

The HL-LHC conditions create unique challenges in terms of high PU levels and high radiation dosage. About 140 PU events per bunch crossing, on average, are expected in the nominal scenario, and up to 200 PU events in the ultimate luminosity scenario. The radiation levels will be unprecedented: for the design integrated luminosity of 3000 fb⁻¹, a 1 MeV neutron equivalent fluence of $2.3\times {10}^{16}\,{n}_{\mathrm{eq}}\,{\mathrm{cm}}^{2}$ and a total ionizing dose of 12 MGy (1.2 Grad) is expected at the centre of the detectors, where the innermost silicon pixel tracking layers will be installed.

To meet the challenges of the HL-LHC operating conditions, and to fully profit from its physics capabilities, comprehensive upgrade programmes are planned for both the ATLAS and CMS experiments. This section summarizes the main detector and trigger upgrade plans for each sub-detector component of both experiments.

5.1.1.1. Tracker

5.1.1.2. Calorimetry

5.1.1.3. Muon system

The MS will be upgraded at both experiments to meet HL-LHC conditions, extend geometric coverage, and improve detector performance and trigger capabilities.

CMS upgrade. For the CMS detector, its current MS consists of three different types of muon detectors. In the barrel region, drift tubes (DTs) are installed along with resistive plate chambers (RPCs). In the endcaps, there are cathode strip chambers (CSCs) together with RPCs. At the HL-LHC, the existing muon detectors will be improved with upgraded electronics to enable 40 MHz readout, as well as improve the timing resolution from the current 12.5–1 ns [350]. New muon detectors, namely gas electron multipliers and a new version of RPCs, will be added to the endcaps, covering the regions of $1.6\lt | \eta | \lt 2.4$. Additional muon chambers, labeled ME0, will cover the very forward regions of $2.4\lt | \eta | \lt 2.8$, a region also covered by the upgraded inner tracker. This will be used for the muon trigger at L1. The additional muon detectors are essential to achieve a high trigger efficiency with an acceptable rate, especially in the forward region. The additional hits in the new endcap muon stations, combined with improved algorithms, permit efficient triggering on displaced muon tracks even in the harsh environment of the HL-LHC.

ATLAS upgrade. Most of the front-end and detector readout of the ATLAS MS, including the trigger electronics for the RPC, thin gap chambers (TGCs), and monitored drift tube (MDT) chambers, will be replaced to face the higher trigger rates and longer latencies necessary for the new Level-0 (L0) trigger required by the HL-LHC conditions. The MDT chambers will be integrated into the L0 trigger in order to sharpen the momentum threshold. Some of the MDT chambers in the inner barrel layer will be replaced with new, small-diameter MDTs. Additional RPC chambers will be installed in the inner barrel layer to increase the acceptance and robustness of the trigger, and some chambers in high-rate regions will be refurbished. New TGC triplet chambers in the barrel–endcap transition region will replace the current TGC doublets to suppress the high trigger rate from random coincidences in this region. The electronics of all the sub-detectors will need to be replaced due to obsolescence, aging, and radiation damage. During the Phase 1 upgrade (to take place from 2019 to 2021) the new small wheel chambers will replace the CSC and the MDT chambers of the innermost endcap wheel by micromegas and small-strip TGCs. The replacement of the MDT front-end readout will address the trigger rate and latency requirements of the TDAQ system in Phase 2 and allow the use of MDT hit information to improve the muon ${p}_{{\rm{T}}}$ resolution in the L0 trigger. Additionally, in the upgraded detector all data from the barrel and endcap detectors will be transmitted to FPGAs at L0, which can be used to implement more advanced and flexible algorithms for muon reconstruction, including the use of neural networks and/or dedicated tracking for non-pointing muons [354].

Some LLP scenarios (e.g. HV models [66]) predict muon-jet final states, which result in collimated muons that are not identified with high efficiency by the current triggers (see section 3.2). In figure 18, the opening angle between muons in a HV model is shown, for a particular combination of particle masses and parameters. The di-muon separation is much smaller than the current system can resolve (approximately 0.2 in Δϕ(μ, μ)). In the no-upgrade scenario, these can only be recorded by the single muon trigger. In the upgraded scenario, a dedicated trigger is under development for a dimuon trigger with a ${p}_{{\rm{T}}}$ threshold of ≈ 10 GeV.

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5.1.1.4. Timing detector

5.1.1.5. Trigger

The ability of the detectors to reconstruct tracks and find vertices with high precision and efficiency in a high-density environment underlies the experimental reach for displaced objects. This section reviews the ATLAS and CMS experiments' projected tracking performance at the HL-LHC, highlighting improvements and new features with the upgrades.

5.1.2.1. CMS performance

L1 tracking. With the aforementioned tracker and L1 track trigger upgrades, the CMS experiment will be able to do track finding at L1 as well as offline at HL-LHC. Both L1 and offline tracking performance are discussed here.

All L1 tracking studies have been performed assuming 3 GeV stub ${p}_{{\rm{T}}}$ thresholds. In figure 19, the L1 tracking efficiency for prompt muons and electrons for $t\bar{t}$ events in a scenario with 200 PU interactions per bunch crossing, on average, is presented. The tracking efficiency for muons exhibits a sharp turn-on at the 3 GeV stub ${p}_{{\rm{T}}}$ threshold, and saturates at approximately 98%. The tracking efficiency for electrons turns on more slowly and flattens out at 90%, mostly due to interaction with the detector material.

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In figure 20, the L1 tracking resolutions of the ${p}_{{\rm{T}}}$ and z₀ parameters of muons with ${p}_{{\rm{T}}}\gt 10\,\mathrm{GeV}$ in $t\bar{t}$ events is shown for various average PU scenarios. The resolutions are defined in terms of an interval centered on the residual distribution that contains 68% or 90% of the tracks. Loss in tracking efficiency due to truncation effects (where there is insufficient time to transfer all the stub data) is determined from hardware and emulation to be at the level of 10⁻³ when considering $t\bar{t}$ samples with a PU rate of 200. As expected, resolutions degrade at forward pseudorapidity due to a corresponding increase in multiple scattering. In general, L1 parameter resolutions are excellent, which will provide for robust trigger object matching and charged particle reconstruction in the L1 trigger.

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Offline tracking. Preliminary results on the offline tracking performance over the full acceptance of the CMS tracker are excellent, with further improvements expected as the detector design and simulation algorithms are optimized. In figure 21, the resolution of the transverse momentum and the transverse impact parameter for single muons with ${p}_{{\rm{T}}}=10\,\mathrm{GeV}$ as a function of the pseudorapidity, both with the current detector and after the implementation of the HL-LHC upgrades, is shown. The better hit resolution of the HL-LHC tracker and the reduction of the material budget result in a significantly improved ${p}_{{\rm{T}}}$ resolution. The transverse impact parameter resolution is also improved with respect to the current detector, ranging from below 10 μm in the central region to about 20 μm at the edge of the acceptance.

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For $t\bar{t}$ events, the efficiency to identify the PV correctly is ∼95% at an average PU level of 140, and ∼93% at an average PU level of 200. The vertex algorithm used is the same as the one used in Run 2 for a PU of about 35, therefore it is not yet optimized for vertex reconstruction at very high PU. In figure 22 the resolution of the vertex position in the x, y, and z coordinates is shown as a function of the number of tracks associated to the vertex. The vertex position resolution is almost independent of the amount of PU in the event and the longitudinal resolution is only 50% worse than the transverse one, as expected given the pixel dimensions of the inner tracker modules.

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Given that the CMS HLT tracking is based on the offline tracking code, a similar level of performance is expected. Because of HLT time constraints, a parallelization of the algorithms is already under development and will be applied also in the HLT track reconstruction at HL-LHC.

5.1.2.2. ATLAS performance

Excellent tracking performance is also expected with the ITk upgrade of the ATLAS experiment for the HL-LHC era. The left panel of figure 23 shows the track reconstruction efficiency for jets in $Z^{\prime} \to \bar{t}t$ events with 200 PU for different η ranges. The right panel of figure 23 shows the fake rate for reconstructed tracks in $t\bar{t}$ events, and there is clearly substantial improvement over the Run 2 detector performance along with the improved coverage in the forward region.

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In figure 24, the resolution of the transverse momentum and the longitudinal impact parameter for single muons with various ${p}_{{\rm{T}}}$ values is shown as a function of the pseudorapidity both with the current detector and projections for after the HL-LHC upgrade using digital clustering to find the tracks. The improvement is even more marked with analogue clustering: the transverse and longitudinal impact parameter resolutions are shown for different pixel pitches in figure 25.

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Searches for LLPs are well motivated by various classes of extensions of the SM, discussed at length in chapter 2.2. Often, the production cross section for such processes is expected to be very small. The HL-LHC will allow for the collection of much larger data sets needed to reach better sensitivity to such BSM scenarios. The prospects are further strengthened with detector and trigger upgrades. This section discusses these potential improvements, and presents sensitivity projections on a number of benchmark LLP search channels with the aforementioned upgrades at the HL-LHC.

5.1.3.1. Heavy stable charged particles in CMS

A number of new physics scenarios give rise to HSCPs with long lifetimes that move with subrelativistical speed through the detector, heavily ionizing the sensor material as they pass through. In split SUSY models, the supersymmetric particles known as the stau ($\tilde{\tau }$) and the gluino ($\tilde{g}$) can have such characteristic signatures. The relevant simplified models are described in sections 2.4.2–2.4.3, and current searches are described in section 3.5.1.1.

Sensitivity projection with tracker upgrade. Depending on the mass and charge of the new particles, HSCPs experience anomalously high energy losses through ionization (dE/dx) in the silicon sensors with respect to the typical energy losses of SM particles, as can be seen in figure 26 (left). At the CMS experiment, the current strip tracker features analog readout. Furthermore, the pixel detector featured analog readout during Phase 0 in 2016 and before, and currently features digital readout during Phase 1, which started at the beginning of the 2017 LHC run. Therefore, these detectors allow for excellent dE/dx measurements.

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At the HL-LHC, the upgraded CMS inner pixel detector will continue providing dE/dx measurements, enabled by its time-over-threshold readout, while the outer tracker cannot provide such information, given that the readout is binary. To increase the sensitivity for signatures with anomalously high ionization loss, a second, programmable, threshold has been implemented in the short strip ASICs of the PS modules of the outer tracker, and a dedicated readout bit signals if a hit is above this second threshold.

Searches for HSCPs can thus be performed by measuring the energy loss in the inner pixel detector and by discriminating HSCPs from minimum ionizing particles based on the 'HIP flag' in the outer tracker. The threshold of the minimum ionization needed to set the HIP flag is an adjustable parameter in each PS module independently. A threshold corresponding to the charge per unit length of 1.4 MIPs, resulting from preliminary optimization studies, is used in the simulation, and the gain in sensitivity obtained by using the HIP flag is studied.

An estimator of the degree of compatibility of the track with the MIP hypothesis is defined to separate candidate HSCPs from tracks from SM background sources. The high resolution dE/dx measurements provided by the inner pixel modules are used for the computation of the dE/dx discriminator. The tracks in background events have a low number of HT clusters with HIP flag, compared to those observed for tracks in HSCP signal events and slow-moving protons and kaons in minimum bias events.

In figure 26 (right), the performance of the discriminator is shown by evaluating the signal versus background efficiency curves to identify tracks from signal events and reject those originating from backgrounds. The performance curves are evaluated for two different strategies for the discriminator: the dE/dx discriminator, which relies solely on the inner pixel modules (dE/dx-only, ignoring the HIP flags), and a recomputed discriminator which includes the HIP flags from the outer tracker PS modules (dE/dx + HIP flags). The signal versus background efficiency performance curves demonstrate that for a background efficiency of 10⁻⁶, analogous to the current analysis performance, the ${\rm{d}}E/{\rm{d}}x+$ HIP-based discriminator leads to an expected signal efficiency of 40%, around 4–8 times better than the dE/dx-only discriminator. In the dE/dx-only scenario, the efficiency for the HSCP signal is about 8 times smaller than that obtained in current data. The inclusion of the HIP flag for the PS modules of the Outer Tracker restores much of the efficiency, so that the same sensitivity as in Phase 1 will be realized with about four times the luminosity of Phase 1. The Phase 1 sensitivity will be surpassed with the full expected integrated luminosity of the HL-LHC. This study demonstrates the critical impact of the HIP flag in restoring the sensitivity of the CMS tracker for searches for HIPs in the HL-LHC era.

Additionally, the current CMS inner pixel detector provides measurements of charge deposits in each pixel up to 9600 electrons over a range of 4 bits in the digitizer. While it may be difficult to increase the number of bits used to store the charge information due to data rate constraints, it is possible to adopt a dual-slope mapping from charge deposit to ADC counts in the digitizer, which will preserve the granularity for lower charge deposits, while giving more information for HIPs such as HSCPs. This option is currently being studied to evaluate the potential improvement to dE/dx measurements. Furthermore, tuning of the HIP flag threshold may bring additional improvements.

HSCP trigger with muon detector upgrade. The upgrade of the RPC system will allow the trigger and identification of slowly moving particles by measuring their TOF to each RPC station with a resolution of ${ \mathcal O }(1)$ ns. The new RPC detectors have a two-end strip readout, which provides precise measurements of the hit position in the local y or the global η coordinate. The speed of muon-like particles and the time (bunch crossing) of their origin will be computed with a fast algorithm to be implemented in the Level-1 trigger at the HL-LHC.

The RPC detectors are synchronized to register muons moving at the speed of light with a local time equal to zero with respect to the collision event that produced the trigger. Slow-moving particles, as HSCPs, will arrive with a delay depending on their speed as shown in figure 27. This time delay, measured by each RPC layer crossed by the HSCP, is exploited in order to trigger on and reconstruct such particles.

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The principles of the proposed HSCP trigger algorithm are illustrated in figure 28. In this figure, the vertical axis is the time of signals measured in RPC chambers, as synchronized so that muons moving nearly at the speed of light from a particular collision are measured at the time of the collision. The horizontal axis is the distance from the collision point to the position of the RPC at which the time is measured. The diagram shows three successive bunch crossings, two of which contain muons represented at horizontal lines. The diagram also shows the RPC time measurements from two HSCPs having slopes different from zero due to their traveling significantly slower than the speed of light. The time delay Δt is related to the speed v of an HSCP via the following equation:

$$\begin{eqnarray}&&{\rm{\Delta }}t=d\left(\displaystyle \frac{1}{v}-\displaystyle \frac{1}{c}\right).\end{eqnarray} \tag{ 5.1 }$$

Here d is the distance between the IP and the point where an HSCP crosses an RPC. For RE4/1 chambers and β = v/c = 0.2, the delay time is > 6 bunch crossings, comparable to 150 ns.

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A penetrating charged particle leaves a trail of hits in RPC chambers along its trajectory. The TOF can be computed in each RPC station with respect to a number of bunch crossing hypotheses. Should there be a common velocity solution, derived from equation (5.1), with β < 0.6, a trigger is formed. For β > 0.6, the delays are small and can be handled by the Phase 1 trigger. The performance of this algorithm has been studied with the CMS full simulation. All the detector effects (e.g. electronics jitter, signal time propagation along strips) are considered. A particle-speed measurement resolution is shown in figure 29 (right) for the case of 25 ns signal sampling time (Phase 1) and 1.56 ns sampling time provided with the upgraded RPC Link Board System. For both plots, an HSCP signal is shown.

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The efficiency of the RPC-HSCP algorithm as a function of β is studied and compared with the standard L1 muon trigger. The results are shown in figure 29 (right). The current CMS-HSCP Phase 1 trigger performs well down to β ≈ 0.75. The upgraded RPC Link Board System will allow for the triggering, at the correct bunch crossing, on possible HSCPs with velocities as low as β ∼ 0.25.

Possible improvements for this trigger proposal in the β measurement could be achieved by matching tracks in the track trigger to the HSCP muon trigger.

5.1.3.2. Displaced muons in CMS

Many BSM theories predict particle decays with displaced muon or muon pairs in its final state, such as dark SUSY and GMSB with smuons. In order to demonstrate the physics potential of displaced muons at the HL-LHC with the CMS detector, a particular SUSY model is selected where the displaced signature consists of a dimuon final state emerging from the decay of heavy sparticles (smuons). Searches for the direct production of heavy sparticles with long lifetimes are difficult in the present LHC runs, owing to small cross sections and limited integrated luminosity, and will only become possible at the HL-LHC.

In GMSB models, smuons can be (co-)NLSPs (next to lightest supersymmetric particles) and decay to a muon and a gravitino [360]. When the slepton is long lived, the final state signature is two displaced oppositely charged muons and significant missing transverse energy. The smuon pair production has the advantage that it can be characterized by a very clean final state topology, and we will therefore focus on the process $q\bar{q}\to \widetilde{\mu }\widetilde{\mu }$, where the two smuons decay far from the primary interaction vertex. For this process, the muon $| {d}_{0}|$ can reach up to approximately one meter (or longer) for sufficiently large lifetimes, as shown in figure 30 (left). Figure 30 (right) compares the number of hits created by these displaced muons in the CMS MS in Phase 2 and the current CMS detector. The hits plotted here are those associated with the DSA muon tracks, which is a muon track reconstruction algorithm specifically designed for displaced muons that can only be reconstructed in the MS [335].

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Standard triggers and reconstruction algorithms that use the position of the PV will not efficiently reconstruct tracks with large impact parameters. Consequently, triggering on and reconstructing muons produced far from the IP is challenging and requires dedicated triggers and reconstruction algorithms. The upgrades to the MS in CMS, as well as the L1 tracking capabilities, significantly improve the experiment's ability to search for displaced muons at the HL-LHC.

Triggering on displaced muons. The momentum resolution of the L1 muon trigger for muons coming from the PV will be greatly improved by adding information from the L1 track trigger, discussed previously. The L1 track trigger can also be directly combined with trigger primitives at the first stage of the muon track-finder electronics; this would mirror the offline reconstruction of 'Tracker Muons' which improve the efficiency for very low-${p}_{{\rm{T}}}$ muons, especially in the barrel region.

To trigger on both prompt and non-prompt muons effectively at L1, a SA L1 muon generates two ${p}_{{\rm{T}}}$ measurements for each muon, prompt and non-prompt, which are matched with L1 tracks. If the track match is successful, the L1 track trigger ${p}_{{\rm{T}}}$ is used and a prompt candidate is formed. If the match is unsuccessful and the muon is not vetoed by L1 tracks, the non-prompt L1 muon ${p}_{{\rm{T}}}$ is used to form a displaced muon candidate. Figure 31 shows good performance for displaced muons with this method, i.e. there is a reasonably high efficiency and a trigger rate for a single muon trigger of around 10 kHz under HL-LHC conditions. Further improvements to the algorithm are underway to accommodate high PU conditions. The upgrade of the RPC system will allow slowly-moving particles to pass the trigger and be identified by measuring their TOF to each RPC station with a resolution of ${ \mathcal O }(1)\,\mathrm{ns}$. The speed of muon-like particles and the time (bunch crossing) of their origin will be computed with a fast algorithm to be implemented in the L1 trigger for the HL-LHC.

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Reconstruction. A dedicated muon reconstruction algorithm was designed for non-prompt muons that leave hits only in the MS. This DSA algorithm is seeded by groups of track segments in the muon chambers. For each seed, a muon track is reconstructed with the same Kalman-filter technique as for the standard SA muon reconstruction algorithm, but without constraining the IP. Figure 30 (right) shows the distribution of the number of hits in the Run 2 and HL-LHC detectors for displaced muons. The impact of the new stations is clearly visible. The charge mis-identification probability is expected to further decrease with the additional hits.

Sensitivity projection with a GMSB model. To study the impact on physics sensitivity, a particular GMSB model is selected where the displaced signature consists of a dimuon final state plus gravitinos, emerging from the decay of heavy long-lived sparticles (smuons), where the gravitinos escape detection. This maps to the direct pair production simplified model with neutral LLP decays to muon + invisible in section 2.4. This signal can serve as a proxy for other models with two LLPs decaying into muons. The final-state signature is then given by two displaced, oppositely-charged muons and significant ${{/}\!\!\!\!{E}}_{{\rm{T}}}$. Example LLPs with cτ = 10, 100, 1000 mm and several mass hypotheses (0.2, 0.5, 1 TeV) are simulated.

The main background for this search comes from multi-jet production (QCD), $t\bar{t}$ production, and Z/DY → ℓℓ events where large impact parameters are (mis)reconstructed. Cosmic-ray muons have been studied in Run 2 and these studies can be directly applied to Phase 2 running. In the barrel, they are efficiently rejected by the timing of the hits in the upper leg. Cosmic-ray muons do not originate at the vertex and therefore pass the upper-barrel sectors in reverse direction from outside in. The fraction of cosmic-ray muons in the endcaps is negligible.

Given the very low cross section of the signal process, it is essential to reduce the background efficiently. The best background discriminator is the impact parameter significance d₀/σ(d₀) ≥ 5. Given the signal kinematics, the muons from a signal process are expected to move in roughly opposite directions and ${{/}\!\!\!\!{E}}_{{\rm{T}}}$ can be expected to be larger than 50 GeV. After this selection the signal efficiency is about 4%–5% for cτ ≈ 1000 mm, nearly independent of the smuon mass, and 10⁻⁵–10⁻⁴ for QCD, $t\bar{t}$, and DY backgrounds.

In figure 32, the expected exclusion limits are shown for the GMSB model in which the smuon is a (co-)next-to-lightest supersymmetric particle (NLSP, where 'LSP' indicates the lightest supersymmetric particle), for the predicted cross section as well as for a factor 100 larger cross section. The exclusion limits are shown as functions of smuon mass in figure 32 (left) and decay length in figure 32 (right).

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The sensitivity depends on cτ because shorter decay lengths shift the signal closer to background. In figure 32 (right), the resulting physics sensitivities in terms of production cross section for the HL-LHC, normalized to 3000 fb⁻¹, are shown for the dedicated reconstruction of displaced muons and for the standard reconstruction. Also shown is the expected sensitivity at the end of Phase 1. Systematic uncertainties for the Phase 1 scenario are taken from current Run 2 analyses and adapted for expected HL-LHC conditions based on the assumptions of reduced systematics described in [361]. Clearly, only the HL-LHC will allow this process to be studied. The expected exclusion limit is around 200 GeV for cτ = 1000 mm with 3000 fb⁻¹. This also illustrates the importance of keeping lepton trigger thresholds at several tens of GeV, even in the environment of 200 PU interactions per bunch crossing. Similarly, the discovery sensitivity is assessed assuming that a signal is present in data, and is shown as a function of smuon decay length in figure 33.

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Sensitivity projection with a dark SUSY model. The analysis presented above was reinterpreted using a Dark SUSY model [30, 155], in which an additional dark U_D(1) symmetry is added as a supersymmetric SM extension. Breaking this symmetry gives rise to an additional massive boson, the so-called dark photon (γ_D), which couples to SM particles via a small kinetic mixing parameter . If is very weak, the lifetime of the dark photon can range from a few millimeters up to several meters. The lower , the longer is the dark photon lifetime which then decays displaced from the PV. A golden channel for such searches is the decay to displaced muons.

In the model studied here [362], dark photons are produced in cascade decays of the SM Higgs boson that would first decay to a pair of MSSM-like lightest neutralinos (n₁), each of which can decay further to a dark sector neutralino (n_D) and the dark photon.

For the branching fraction BR(H → 2γ_D + X), where X denotes the particles produced in the decay of the SM Higgs boson apart from the dark photons, 20% is used. Neutralino masses m(n₁) = 50 GeV and m(n_D) = 1 GeV are assumed. Final states with two and four muons are included in the analysis. In the former case, one dark photon decays to a pair of muons while the other dark photon decays to some other fermions (2-muon final state). In the latter case, both dark photons decay to muon pairs (4-muon final state).

The main background for this search comes from multi-jet production (QCD), ttbar production, and Z/DY → ℓℓ events where large impact parameters are (mis)reconstructed. Cosmic ray muons can travel through the detector far away from the PV and mimic the signature of displaced muons. However, thanks to their striking detector signature, muons from CRs can be suppressed by rejecting back-to-back kinematics.

For each event, at least two DSA muons are required. If more than two, the ones with the highest ${p}_{{\rm{T}}}$ are chosen. The two muons must have opposite charge (${q}_{\mu ,1}\cdot {q}_{\mu ,2}=-1$) and must be separated by ${\rm{\Delta }}R=\sqrt{{\rm{\Delta }}{\phi }^{2}+{\rm{\Delta }}{\eta }^{2}}\gt 0.05$. The three-dimensional angle between the two displaced muons is required to be less than π − 0.05 (not back-to-back) in order to suppress CR backgrounds. Additionally, ${{/}\!\!\!\!{E}}_{{\rm{T}}}\geqslant 50\,\mathrm{GeV}$ is imposed to account for the dark neutralinos escaping the detector without leaving any signal.

In order to discriminate between background and signal, the three-dimensional distance from the PV to the point of closest approach of the extrapolated displaced muon track, called R_Muon, is used. The event yield after full event selection of both selected muons as a function of ${R}_{\mathrm{Muon}-1}$ and ${R}_{\mathrm{Muon}-2}$ is used to search for the signal. The left panel of figure 34 shows ${R}_{\mathrm{Muon}-1}$ of the first selected muon for signal and background samples.

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The search is performed using a simple counting experiment approach. In presence of the expected signal, significance of the corresponding event excess over the expected background is assessed using the likelihood method. In order to evaluate the discovery sensitivity the same input is used as in the limit calculation, now with the assumption that one would have such a signal in the data. The discovery sensitivity is shown in the two-dimensional ${m}_{{\gamma }_{D}}$–$c\tau$ plane in the right panel of figure 34. This search is sensitive to large decay length of the dark photon.

In absence of a signal, upper limits at 95% C.L. are obtained on a signal event yield with respect to the one expected for the considered model. A Bayesian method with a uniform prior for the signal event rate is used and the nuisance parameters associated with the systematic uncertainties are modeled with log-normal distributions. The resulting limits for the Dark SUSY models are depicted in figure 35. While the results shown in the left panel of figure 35 are for a dark photon with a decay length of 1 m as a function of the dark photon mass, the right panel of figure 35 shows the results for a dark photon mass of 20 GeV as a function of the decay length [362].

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5.1.3.3. Displaced photons at CMS

A number of new physics scenarios predict new particles that, upon decay, result in displaced photons in the final state (see sections 2.4 and 3.4). At the CMS experiment, with the scintillating crystal design of the ECAL that provides excellent resolution but lacks pointing capability, the photon arrival time in the ECAL is the main observable used to distinguish signal from background in displaced photon searches.

One benchmark model for displaced photon searches is the GMSB model where the lightest neutralino (${\tilde{\chi }}_{0}^{1}$) is the NLSP, can be long-lived, and decays to a photon and a gravitino ($\tilde{G}$), which is the LSP, as illustrated in figure 36 (left). For a long-lived neutralino, the photon from the ${\tilde{\chi }}_{0}^{1}\to \tilde{G}+\gamma$ decay is produced at the ${\tilde{\chi }}_{0}^{1}$ decay vertex, at some distance from the beam line, and reaches the detector at a time later than that of prompt, relativistic particles produced at the IP. The time of arrival of the photon at the detector can be used to discriminate the signal from the background. The aforementioned upgrade to the ECAL electronics in the barrel region, and the HGCAL upgrade in the endcaps, will improve photon timing resolution at HL-LHC by an order of magnitude to as little as ∼ 30 ps for photons with ${p}_{{\rm{T}}}$ of tens of GeV or above, hence significantly improve the experimental reach of displaced photon searches.

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Moreover, the proposed MTD will be able to provide another dimension of information to reconstruct LLP decays. The TOF of the photon inside the detector is the sum of the TOF of the neutralino before its decay and the TOF of the photon itself, until it reaches the detector. Since the neutralino is a massive particle the latter is clearly negligible with respect to the former. In order to be sensitive to short neutralino lifetimes of order 1 cm, the performance of the measurement of the photon TOF is a crucial ingredient of the analysis. Therefore, the excellent resolution of the MTD apparatus can be exploited to determine with high accuracy the TOF of the neutralino, and similarly the photon, also in case of a short lifetime.

An analysis has been performed at generator level in order to evaluate the sensitivity power of a search for displaced photons at CMS in the scenario where a 30 ps timing resolution is available from the MTD [351]. The events were generated with Pythia 8 [219], exploring neutralino lifetimes (cτ) in the range 0.1–300 cm. The values of the Λ scale parameter were considered in the range 100–500 TeV, which is relevant for this model to be consistent with the observation of a 125 GeV Higgs boson. After requiring the neutralino to decay within the CMS ECAL acceptance and the photon energy being above a 'trigger-like' threshold, the generator-level photon TOF was smeared according to the expected experimental resolutions. A cutoff at a photon time greater than 3σ of the timing resolution is applied and the 'signal region' is assumed to be background free to estimate the sensitivity. The signal efficiency of such a requirement is computed and translated, assuming the theoretical cross sections provided in [66], to an upper limit, at 95% C.L., on the production cross section of the ${\tilde{\chi }}_{0}^{1}\to \tilde{G}+\gamma$ process.

In figure 36 (right), the analysis sensitivity in terms of the Λ scale (and therefore of the neutralino mass) and lifetime is shown for three different assumptions on the timing resolution. The 300 ps resolution is representative of the TOF resolution consistent with current CMS detector performance. The 180 ps resolution is representative of the TOF resolution of the upgraded CMS detector without the MTD, in which case the TOF measurement will be dominated by the time spread of the luminous region. The vertex timing provided by the MTD detector will bring the TOF resolution to about 30 ps. As visible in the figure, a full-scope upgrade of the CMS detector with photon and track timing will provide a dramatic increase in sensitivity at short lifetimes and high masses, even with the first 300 fb⁻¹ of integrated luminosity.

5.1.3.4. Displaced jets in ATLAS

Neutral LLPs that can decay into jets displaced from the proton–proton IP arise in many BSM theories (see chapter 2 for an extensive discussion). For example, in hidden sector models a new set of particles and forces is proposed that is weakly coupled to the SM via a communicator particle. The hidden sector is otherwise invisible to the SM sector, but its particles (some of which can be long-lived) may decay to SM particles via the communicator. The lifetimes of these LLPs are typically unconstrained and could be long enough for the LLPs to decay inside the ATLAS detector volume. Such particles produce unique signatures which may have been overlooked by more traditional searches for new physics. One ATLAS search for such displaced jet signatures focuses on LLPs which decay in the ATLAS HCal and consequently deposit most of their energy there and very little or none in the ECAL, and also have few or no charged tracks pointing at the hadronic energy deposits. A signature-driven trigger that optimizes the acceptance for this class of events is required for the online selection.

The existing ATLAS analysis described in section 3.1 can likely be improved by planned upgrades by using HCal information splitting the B-C layers in the calorimeter to identify the LLP decay position. The splitting between B-C layers will provide more information on the longitudinal shower profile, see figure 37.

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This analysis uses a hidden sector benchmark model and considers the decay of a heavy boson to two long-lived neutral scalars; this maps to the simplified model with Higgs boson production of hadronically decaying LLPs in section 2.4. The heavy scalar bosons decaying into LLPs have masses ranging from 125 to 1000 GeV, and the LLP scalars have masses ranging between 5 and 400 GeV. Background processes, dominated by QCD dijet production, are suppressed in this analysis by requiring both scalars to decay in the calorimeter. Final results of the sensitivity projections are pending.

5.1.3.5. Disappearing tracks

In the ATLAS experiment, the planned ITk upgrade of the tracking volume for the HL-LHC can be exploited to improve the existing searches for BSM particles with a DT [353].

Such particles are predicted by many well-motivated supersymmetric models such as anomaly-mediated SUSY-breaking scenarios, where the supersymmetric partners of the SM W bosons, the wino fermions, are the lightest SUSY state. In such models, the lightest neutralino and chargino can be nearly mass-degenerate, with a mass splitting around 160 MeV, and the chargino is consequently long lived. The combination of long lifetime and boost when produced in a high-energy collider allows the chargino to leave multiple hits in the traversed tracking layers before decaying. When performing searches for such signatures in ATLAS, selected events are typically required to contain at least one short track, hereafter called a tracklet. To study how such searches can be improved with the ITk upgrade, some assumptions have been made for simulating events and projected detector response. The detector response is parametrised by using response functions based on studies performed with Geant4 simulations of the upgraded detector in high-luminosity PU conditions.

The tracklet reconstruction efficiency for signal charginos as a function of the decay radius inside the detector is shown in figure 38. A 30% systematic uncertainty on the background yields is assumed, as observed for the Run 2 analysis. The expected background is largely dominated by fake tracklets due to random crossings.

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Expected limits at 95% C.L. are shown in figure 39 as a function of the chargino mass and lifetime for a pure wino and a pure Higgsino LSP scenario. For comparison, the current Run 2 limit for 36.1 fb⁻¹ in the wino LSP scenario is also shown. The HL-LHC dataset of 3000 fb⁻¹ extends the sensitivity of neutrinos and charginos up to 250 GeV, assuming a pure Higgsino scenario.

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5.1.3.6. Displaced vertices in ATLAS

Massive, LLPs with lifetimes of the order of O(10) ps to O(10) ns can decay inside the inner tracker into charged and stable particles. The products of these decays are reconstructed as tracks with measurably distant impact parameters with respect to the IP. The reconstruction of such displaced tracks is very challenging compared to the track reconstruction of prompt particles, due to fewer hits along the track and a larger parameter phase space for track finding. In order to identify a DV, one must first identify the tracks from the decaying LLP.

Several physics models predict the existence of long-lived, massive particles. For example, a standard SUSY scenario can contain a gluino with a mass of 2 TeV and a lifetime of 1 ns. The long-lived gluino hadronises into an R-hadron, which then decays into a 100 GeV neutralino and hadrons.

In ATLAS, this topology has been investigated in Run 2 by using a dedicated algorithm for reconstructing DV [255]. The performance expected to be achieved for the ITk upgrade for this signal has been tested with a simplified simulation which has a description of the ITk active sensors and a modeling of the magnetic field. The kinematics and location of the decay products of the R-hadron are injected into the simulation and their trajectories are extrapolated through the detector model. The probability of producing at least seven silicon hits in the ITk geometry is shown in figure 40 for a 2 TeV R-hadron with τ = 1 ns. The increased volume and number of ITk layers leads to improved efficiency for the reconstruction of tracks from DV (and hence the vertices themselves) out to radial distances of up to 550 mm. The increased number of silicon layers also gives more room to veto tracks with missing hits, further suppressing backgrounds.

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5.1.3.7. LLP searches with precision timing at CMS

The CMS MTD will provide new, powerful information in searches for LLPs. In addition to the aforementioned displaced photon search, the additional timing information can be used to provide full kinematic reconstruction of LLP decays, and can be a powerful tool in background suppression.

Possible improvements in the ability to reconstruct LLP mass. A precision MTD allows each reconstructed vertex to be assigned a time and therefore to measure the TOF of LLPs between primary and secondary vertices. Using the measured displacement between primary and secondary vertices in space and time, the velocity of an LLP in the laboratory frame, ${\vec{\beta }}_{\mathrm{LAB}}^{p}$ (or, equivalently, the boost γ^p), can be measured. In such scenarios, the LLP can decay to fully visible or partially invisible systems. Using the measured energy and momentum of the visible portion of the decay, one can calculate its energy in the LLP rest frame and reconstruct the mass of the LLP, assuming that the mass of the invisible system is known.

This capability can be demonstrated in scenarios where the LLP decay produces a Z boson, which then decays to an electron–positron pair. For example, in the GMSB model where the ${\tilde{\chi }}_{0}^{1}$ couples to the gravitino $\tilde{G}$ via higher-dimension operators sensitive to the SUSY breaking scale, the ${\tilde{\chi }}_{0}^{1}$ may have a long lifetime, and can be produced in top-squark pair production with $\tilde{t}\to t+{\tilde{\chi }}_{0}^{1}$, ${\tilde{\chi }}_{0}^{1}\to Z+\tilde{G}$, $Z\to {ee}$.

Studies with simulated event samples have been performed to estimate the possible improved sensitivity of the search with the CMS MTD upgrade. The events are generated with Pythia 8, and the masses of the top-squark and neutralino are set to 1000 GeV and 700 GeV, respectively. Generator-level quantities are smeared according to the expected experimental resolutions. A position resolution of 12 μm in each of the three spatial directions is assumed for the PV. The secondary vertex position for the electron–positron pair is reconstructed assuming 30 μm position resolution in the transverse direction. The momentum resolution for electrons is assumed to be 2%. Finally, the time resolution of charged tracks at the DV is assumed to be 30 ps.

The mass of the LLP is reconstructed assuming that the gravitino is massless. The fraction of events with separation between primary and secondary vertices exceeding 3σ in both space and time as a function of the MTD resolution is shown in figure 41 (left). The mass resolution, defined as half of the shortest mass interval that contains 68% of events with 3σ displacement is shown in figure 41 (right), as a function of the MTD resolution.

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A similar study has been performed with another SUSY scenario where the two lightest neutralinos and light chargino are Higgsino-like. The light charginos and neutralinos are nearly mass degenerate and may become long-lived as a consequence of the heavy higgsinos. Figure 42 shows the mass resolution as a function of the MTD resolution in this SUSY scenario. In both studies, the additional timing information from the MTD facilitates the reconstruction of the LLP mass, the resolution and efficiency of which are further improved with the excellent timing resolution of the MTD.

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Possible improvement to LLPs searches in general using timing information. Precision timing at CMS will provide a new tool to suppress the background and enhance the reach for LLPs in the HL-LHC era.

A schematic of a typical signal event containing an LLP is shown in figure 43. An LLP, denoted as X, travels a distance ℓ_X into a detector volume and decays into two light SM particles a and b, which then reach a timing layer at a transverse distance ${L}_{{T}_{2}}$ away from the beam axis. In a typical hard collision, the SM particles generally travel very close to the speed of light. Hence, the decay products of X (using particle a as an example) arrives at the timing layer with a time delay of

$$\begin{eqnarray}&&{\rm{\Delta }}t=\displaystyle \frac{{{\ell }}_{X}}{{\beta }_{X}}+\displaystyle \frac{{{\ell }}_{a}}{{\beta }_{a}}-\displaystyle \frac{{{\ell }}_{\mathrm{SM}}}{{\beta }_{\mathrm{SM}}},\end{eqnarray} \tag{ 5.2 }$$

with β_a ≃ β_SM ≃ 1. An ISR jet could easily be present for all processes, and can be used to 'timestamp', i.e. to derive the time of the hard collision at the PV.

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For the CMS MTD located just outside the tracker volume, ℓ_SM/β_SM is about O(1 ns). As a result, with tens of picosecond (ps) timing resolution, a sensitivity to percent-level time delay caused by slow LLP motion, e.g. 1 − β_X > 0.01 with boost factor γ < 7, is expected to be achieved.

A theory study has been done in [363] examining potential gains in sensitivity for hadronic DV reconstruction using timing information. A new trigger strategy for a delayed jet is studied by comparing the prompt jet with ${p}_{{\rm{T}}}\gt 30\,\mathrm{GeV}$ that reconstructs the four-dimensional primary vertex (PV4d) with the arrival time of another jet at the timing layer. The delayed and displaced jet signal, after requiring a minimal decay transverse distance of 0.2 m (${L}_{{T}_{1}}$), will typically not have good tracks associated with it. Consequently, the major SM background is from trackless jets. The origins of this background can be classified into two categories: hard collision from a same vertex (SV), and PU from different vertices. Other types of background such as CRs, beam halo, material interactions, etc, are out-of-time and will become important after most of the hard collision background is removed using selections based on reconstructing vertices and timing delay. Out-of-time backgrounds may have other distinctive features that would allow their effective suppression. While the study in [363] can serve as an optimistic inspiration for increasing LLP sensitivity with timing information, detailed experimental studies are needed to determine the actual sensitivity gain.

The jet faking a displaced signal, behaving as a trackless jet, has an intrinsic time delay Δt = 0. However, due to the limited timing resolution in reconstructing the PV4d, it can have a time spread. The background differential distribution with respect to apparent delay time (Δt) can be estimated as

$$\begin{eqnarray}&&\displaystyle \frac{\partial {N}_{\mathrm{bkg}}{\left(t\right)}^{\mathrm{SV}}}{\partial {\rm{\Delta }}t}={N}_{\mathrm{bkg}}^{\mathrm{SV}}{ \mathcal P }({\rm{\Delta }}t;{\delta }_{t}^{\mathrm{SV}}).\end{eqnarray} \tag{ 5.3 }$$

The time delay selection on Δt reduces such a background through a very small factor of ${ \mathcal P }({\rm{\Delta }}t;{\delta }_{t}^{\mathrm{SV}})$ for large ${\rm{\Delta }}t/{\delta }_{t}^{\mathrm{SV}}$, where ${\delta }_{t}^{\mathrm{SV}}$ is the timing resolution for the SV background, dominant by the timing detector resolution. The LLP signal pays a much smaller penalty factor than the background due to its intrinsic delay.

The background from the PU requires the coincidence of a triggered hard event and objects from a PU (hard) collision whose PV4d fails to be reconstructed and that can mimic a signal. The differential background from PU can be estimated as

$$\begin{eqnarray}&&\displaystyle \frac{\partial {N}_{\mathrm{bkg}}^{\mathrm{PU}}({\rm{\Delta }}t)}{\partial {\rm{\Delta }}t}\simeq {N}_{\mathrm{bkg}}^{\mathrm{PU}}{ \mathcal P }({\rm{\Delta }}t;{\delta }_{t}^{\mathrm{PU}}).\end{eqnarray} \tag{ 5.4 }$$

Similar to equation (5.3), ${\delta }_{t}^{\mathrm{PU}}$ is the timing resolution for the PU background, dominated by the beam spread. The key difference between the background from the PU and the background from the same hard collision is that the typical time spread is determined by the beam property for the former, and by the timing resolution for the latter. They typically differ by a factor of a few, e.g. 190 versus 30 ps for CMS with the current upgrade plan.

Using this estimation, a sensitivity projection is presented with an example signal of a Higgs boson decaying to LLPs with the subsequent decay of the LLPs into $b\bar{b}$ pairs, with only minimal requirements of one low-${p}_{{\rm{T}}}$ ISR jet, with ${p}_{{\rm{T}},j}\gt 30\,\mathrm{GeV}$ and $| {\eta }_{j}| \lt 2.5$, and at least one LLP decay inside the detector. Timing information is used to suppress backgrounds. The 95% C.L. sensitivity is shown in figure 44. The decay branching ratio of the LLP $X\to {jj}$ is assumed to be 100%. The projection with 30 ps timing resolution of the CMS MTD is plotted with thick dashed lines. Compared to other 13 TeV HL-LHC projections (with 3 ab⁻¹ of integrated luminosity) without the timing information (shown in thinner, dotted and dashed lines), it is suggested that the addition of a selection on timing, under the set of assumptions described above, greatly reduces background and improves sensitivity. The possibility of such a significant improvement is enticing; this projection is determined from theoretical studies [363], however, and it remains to be seen whether it is possible to realize these gains in the experiment. For example, the low threshold of the single jet would require timing information at early levels of the trigger, and out-of-time backgrounds could also reduce the gains from timing information. Nevertheless, this high-level theory analysis provides an inspiration to the experimental collaborations to perform more detailed, internal studies that will ultimately determine how realistic the projections are.

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In general, the prospect of improvements in LLP searches at the HL-LHC due to precision timing upgrades for CMS (and ATLAS) remains understudied, and deserves more comprehensive experimental and phenomenological studies, including understanding and reducing out-of-time backgrounds.

5.1.3.8. LLP searches with a level-1 track trigger in CMS

As discussed in section 5.1.1, a central feature of the CMS upgrade at the HL-LHC will be a new silicon outer tracker which allows track reconstruction for every LHC bunch crossing (at a rate of 40 MHz). The ${p}_{{\rm{T}}}$ selection for stubs (hit pairs in the ${p}_{{\rm{T}}}$ modules of the outer tracker) to be read out is determined by the bandwidth from the detector to the back end electronics, and is fixed at about 2 GeV. On the other hand, the choice of track finding algorithm and hardware is still being finalized, and there could be significant benefits to extending the L1 track trigger capabilities to trigger on off-pointing tracks.

To illustrate the case, a simple toy simulation to study rare Higgs boson decays into new particles with lifetimes of order of a few mm has been performed [364]. This study considers all-hadronic final states with low H_T, taking SM Higgs boson decays into four jets as an example. Theoretical motivation to look for such decays is very strong; see section 2.2 for a detailed discussion. In particular, there is currently a blind spot for lifetimes of order 1 cm in searches for new long-lived scalars in Higgs decays, i.e. $h\to \phi \phi$. The goal is to probe very small branching fractions of the Higgs boson, so for this study, ${BR}[h\to \phi \phi \to 4q]={10}^{-5}$ is assumed. For prompt decays, the background is overwhelming, but if the ϕ has cτ of a few mm, the offline analysis has very low backgrounds. The problem is getting such events on tape, in particular through L1. This toy study estimates how an off-pointing track reconstruction at L1 can help. To estimate the efficacy of the approach, the resulting projections are compared with the best alternatives in the absence of an off-pointing track trigger, by using associated Higgs boson production with a W boson that decays leptonically to pass a lepton trigger, or considering L1 calorimeter jets with no associated prompt tracks.

Once these positive results were obtained, a more detailed study using the full Phase 2 simulation of the CMS detector was performed [365]. The more mature exploration found that a plausible extension of the L1 track trigger to tracks with an impact parameter of a few centimeters results in dramatic gains in the trigger efficiency. The gains are even larger for additional heavy SM-like Higgs bosons with the same decay. These results are in agreement with the toy study described above. A few details of the mature study will be described below.

The study focuses on small or moderate decay lengths of the new particles, 1–50 mm, and assumes that the offline selection can remove all SM backgrounds with only a moderate loss of efficiency. While this study focuses on the specific Higgs boson decay to light scalars, the results and the proposed triggers are relevant for a broad spectrum of new physics searches, with or without macroscopic decay lengths.

The authors propose a simple jet clustering algorithm implementable in firmware, and compare it with anti-${k}_{t}$ jets [366] with a size parameter of R = 0.3, as produced by FastJet [367]. This simple algorithm produces a similar performance, in both L1 trigger efficiency and rate, to the full jet clustering using the anti-${k}_{t}$ algorithm.

Then, the performance of an algorithm for reconstruction of tracks with non-zero impact parameter is presented. This approach extends the baseline CMS L1 Track Trigger design to handle tracks with non-zero impact parameter and to include the impact parameter in the track fit. This enhanced design is feasible without greatly altering the track finding approach, but will require more FPGA computational power than the current proposal, which only considers only prompt tracks. Tracks passing the selection are clustered using the same algorithm as described above, and clusters containing tracks with high impact parameters are flagged as displaced jets. Though the baseline design of the L1 Track Trigger currently is optimized to find prompt tracks, these studies show that an enhanced L1 Track Trigger can extend the L1 trigger acceptance to include new BSM physics signals.

For now, the extended L1 track reconstruction is limited to the barrel region. In order to compare the results with prompt and extended track reconstruction, one needs to make a correction for the rapidity coverage: prompt tracks are found in $| \eta | \lt 2.4$, while the extended track algorithm currently only reconstructs tracks in $| \eta | \lt 1.0$. To scale the efficiency for finding track jets to the full $| \eta | \lt 2.4$ range, a scale factor based on efficiency in the full η range and the central η range was used. The scale factor was comparable to the increase in L1 rate.

Figure 45 shows the expected trigger rate as a function of efficiency for the SM and the heavy SM-like Higgs bosons.

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The available bandwith for the triggers described above, if implemented, will be decided as a part of the full trigger menu optimization. Here, two cases are considered: 5 and 25 kHz. The expected event yield for triggers using extended and prompt tracking are shown in figure 46, assuming branching fraction ${ \mathcal B }[h\to \phi \phi ]={10}^{-5}$ for the SM Higgs boson. For the heavy Higgs boson, the expected number of produced signal events is set to be the same as for the SM Higgs by requiring ${\sigma }_{{pp}\to h(250)}{ \mathcal B }[{\rm{\Phi }}\to \phi \phi ]={10}^{-5}{\sigma }_{{pp}\to h(125)}$.

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For the exotic Higgs decays considered, given the expected total dataset for the HL-LHC of 3 ab⁻¹, and assuming a branching fraction of 10⁻⁵, CMS would collect ${ \mathcal O }(10)$ events, which should be sufficient for discovery. A plausible extension of the L1 track finder was considered, to select tracks with impact parameters of a few cm. That approach improves the yield by more than an order of magnitude. The gains for the extended L1 track finding are even larger for the events with larger H_T, as demonstrated by the simulations of heavy Higgs boson decays.

The higher data rate and more powerful machinery in the high-luminosity era bring new prospects to LLP searches. Searches that are too challenging for the current machine may become feasible with the HL-LHC upgrades, and it is important to explore such possibilities to the full extent. Existing search methods, triggering, and reconstruction algorithms should also be updated to take full advantage of the new hardware capabilities. As the upgrade scope is being defined and finalized in the near future, it is of particular importance to evaluate the physics cases, which will also motivate the upgrade and inform its designs.

5.1.4.1. New studies for the HL-LHC

5.1.4.2. New detectors at future collider

In LHC Run 3, LHCb plans to take data at an instantaneous luminosity of $2\times {10}^{33}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, a factor of five larger than the current luminosity. The LHCb detector needs to be upgraded to cope with the higher radiation dose and, most importantly, to avoid the saturation of the trigger rate and exploit the higher luminosity. The main bottleneck in the current trigger is in the first stage, which reduces the accepted rate from 30 to 1 MHz at hardware level. For the upgrade, the hardware trigger will be removed and the full event will be read out at the bunch crossing rate of the LHC (40 MHz), with a flexible software-based trigger.

In table 4 the current and upgraded conditions of the detector are summarised. To cope with the larger occupancy and higher rate of the upgraded detector, the electronics of all of the sub-detectors must be upgraded, and some sub-detectors must be fully replaced. For example, the tracking system, which plays a crucial role in LLP searches, must be replaced.

Table 4.  LHCb current and upgraded operating conditions [374]. Instantaneous luminosity ${ \mathcal L }$, integrated luminosity ${\int }_{}{ \mathcal L }$ (including previous runs), pp collision energy $\sqrt{s}$ and average number of visible proton interactions μ are listed.

	Current	Upgrade 1a	Upgrade 1b	Upgrade 2
${ \mathcal L }/({\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1})$	4 × 1032	2 × 1033	2 × 1033	2 × 1034
${\int }_{}{ \mathcal L }$	8 $\,{\mathrm{fb}}^{-1}$	23 $\,{\mathrm{fb}}^{-1}$	50 $\,{\mathrm{fb}}^{-1}$	300 $\,{\mathrm{fb}}^{-1}$
$\sqrt{{\rm{s}}}$	7, 8, 13 TeV	14 TeV	14 TeV	14 TeV
μ	∼1	∼5	∼5	∼50

The upgraded tracking system consists of the VELO, surrounding the IP, the Upstream Tracker, a TT placed before the magnet, and the scintillating fibers tracker (SciFi), three stations after the magnet. In the VELO [375], the current strips will be replaced by pixel detectors, with a custom developed ASIC (VeloPix) able to cope with a maximum hit rate of 900 Mhits/s/ASIC. The Upstream Tracker [376] is composed of four silicon micro-strip planes, with finer granularity and larger acceptance compared to the current tracker. Each station of the SciFi has four planes of 2.5 m long scintillating fibres read out by silicon photo-multipliers.

The upgrade components most important for LLP searches are the VELO, the tracking and the software trigger. In the following subsections a brief description of the design and capabilities is given for each.

5.2.1.1. VELO upgrade

The VELO plays a fundamental role in LLP searches at LHCb: due to the large boost particles typically experience in the forward direction, a precise measurement of the LLP vertex position allows LHCb to efficiently reject tracks that belong to a different b or c vertex (see section 4.2).

In upgrade conditions, the number of tracks and primary vertices will increase by about a factor of five, making it much more difficult to identify DV close to the beam-line; it is an additional challenge to accomplish this in real time. The VELO was thus completely redesigned [375] to cope with the new expected high-luminosity conditions, maintaining high physics performance and allowing real-time readout for the software trigger. The new VELO has a pixel rather than strip geometry and its distance from the LHC beams is reduced from 8 to 5 mm. This leads to an improvement in the vertex resolution (see figure 47) and reduces the rate of unphysical (ghost) tracks.

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The pattern recognition efficiency for track reconstruction is superior to the one of the current VELO when evaluated in high-luminosity conditions. Particularly important for LLP searches is the efficiency of track reconstruction as a function of the displacement from the origin along the beam axis. As shown in figure 48, for the upgraded VELO the efficiency approaches 100% and is uniform in a window of 20 cm around the IP, thanks to the new configuration of the modules in the z direction and the shorter distance from the beam. The VELO acceptance degrades quickly after 20 cm in z, giving an upper limit for LLP decay lengths with vertices reconstructible in the VELO. A display of the upgraded VELO geometry and its acceptance in both the forward and backward directions is shown in figure 49.

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Another important metric of detector performance is impact parameter resolution, especially in LLP searches where it can be exploited to reduce the background due to fake tracks. With the upgrade, the impact parameter resolution significantly improves for low-${p}_{{\rm{T}}}$ tracks. For example, the impact parameter resolution along x for tracks with ${p}_{{\rm{T}}}$ of 0.5 $\,\mathrm{GeV}$ is 40 μm in the upgrade versus 70 μm in the current VELO. The replacement of strips with pixel sensors also makes the pattern recognition faster for the same multiplicity. This can be used in the trigger to find tracks and identify DV in the trigger, making it possible to soften or remove inefficient ${p}_{{\rm{T}}}$ requirements.

Real displaced tracks created by interactions in the VELO material can be a significant background to LLP searches (further details are discussed in chapter 4). The total material budget of the upgraded VELO is similar to that of the current detector (with a radiation length of about 20%) and is dominated by interactions in the radio-frequency foil separating the beam vacuum from the vacuum of the sensors. However, the average percentage of radiation length before the first measured point is significantly reduced in the upgrade VELO, passing from 4.6%X₀ in the current design to 1.7%X₀ in the upgraded VELO (where X₀ is the radiation length).

5.2.1.2. Upgraded trigger

The online event selection in the LHCb experiment during the 2010–2018 running period has been performed by a trigger composed of a hardware level (L0), and two software levels: High Level Trigger 1 (HLT1) and High Level Trigger 2 (HLT2). The L0 reduces the rate from 40 MHz (the LHC bunch-crossing rate) to 1 MHz using information from the calorimeter and MSs. Typical requirements in the L0 are ${p}_{{\rm{T}}}\gt 1.4\,\mathrm{GeV}$ for muons and $E\gt 2.5\,\mathrm{GeV}$ for electrons. The software trigger performs a partial event reconstruction at HLT1, reconstructing tracks and primary vertices for any particle down to ${p}_{{\rm{T}}}=500\,\mathrm{MeV}$, followed by a complete event reconstruction at HLT2, reducing further the rate to 12.5 kHz (in LHC Run 2).

In the Phase 1 upgrade, LHCb foresees to run at a luminosity of $2\times {10}^{33}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, about a factor of five larger than that experienced during LHC Run 2. For this reason, a new trigger system, able to fully exploit the LHC potential, has been designed [377, 378]. The upgraded LHCb trigger is based on two paradigms: a triggerless readout and a full software trigger. In addition, as already tested in Run 2, a real-time alignment and calibration will achieve offline-quality reconstruction already in the trigger, allowing a higher signal purity of interesting decay channels. Figure 50 shows the current and the upgraded trigger schemes.

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Triggerless readout and full-software trigger. With the LHCb trigger upgrade, the 1 MHz readout limitation will be removed, allowing the full event rate to be processed in software. This will increase the efficiency for several channels which otherwise would not benefit from the higher luminosity because they would saturate the L0 trigger rate. Figure 51 shows how the rate for non-muonic B decays saturates the L0 trigger with increasing luminosity. Most of these channels saturate the L0 trigger already at the Run 2 luminosity ($4\times {10}^{32}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$). Moreover, a purely software trigger will not be subject to the ${p}_{{\rm{T}}}$ requirements currently applied at the hardware trigger level. Several physics programs involving low-${p}_{{\rm{T}}}$ particles, currently prohibited by of the low L0 efficiency, will therefore become possible.

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Turbo stream. Starting from Run 2, offline-quality alignment and calibration has been applied between the HLT1 and the HLT2 levels. This was made possible by the design of a new dedicated trigger output called Turbo Stream. The event record is written directly from the trigger and processed so that it can be used for physics analysis without the need for offline reconstruction [277]. Several variations of Turbo have been introduced in the last several years. For 2015 data taking, the first version of Turbo allowed only the triggered signal candidate objects to be saved, without keeping the rest of the event and thereby discarding all sub-detector information. While the event size was an order of magnitude smaller than for full stream data, any analysis relying on additional information from the surrounding event could not use Turbo Stream data.

For this reason, full event reconstruction was implemented as Turbo++ in 2016. Finally, a new intermediate solution between Turbo and Turbo++ called Turbo SP (Selective Persistence) was implemented in 2017. With Turbo SP, both the trigger candidate objects and a subset of the other objects in the event are saved. This flexible solution allows the analyzer to choose which objects to save, minimizing the size of the stored event. Once the trigger is upgraded to run purely at the software level, the large majority of LHCb analyses will be moved to Turbo. The reduced event size allows the storage of particle candidates at a high rate, fully exploiting the reduction in ${p}_{{\rm{T}}}$ thresholds due to the removal of the L0 hardware trigger.

Triggers on downstream tracks. Most of the LLP searches at the LHCb experiment use so-called 'long tracks' to reconstruct the candidates, which are tracks where inputs from both the VELO and the TTs are considered. These tracks have an excellent spatial and momentum resolution, and result from an LLP decaying within the VELO region. This is the reason why most of the LLP searches done by LHCb correspond to long-lived candidates with displacements typically up to ${ \mathcal O }$(10) cm, with the VELO tracking algorithm optimized for displacements of up to 20 cm. However, for long-lived candidates with displacements larger than 2 cm, a different type of track which considers information only from the TTs, 'downstream tracks', has to be used instead of the 'long track' type. Unfortunately, these tracks have worse vertex and momentum resolution, limiting the capabilities of LHCb for this displacement range. In order to improve the detector sensitivity in the displacement ranges between 20 and 200 cm, a proposal to develop new trigger lines to select 'downstream tracks' is being studied [378]. An interesting idea which can help to achieve this task and to significantly reduce the CPU computing time is the implementation of a system of specialized processors used to rapidly find the downstream tracks through look-up tables, and present these tracks to the software trigger in parallel with all the raw detector information in the event. This system, named 'retina', is being studied and has its own R&D programme [381].

The much higher luminosity and improved capabilities of the upgraded LHCb detector are expected to significantly improve the capabilities for LLP searches in LHC Run 3. In the following sections, the projected sensitivities to several benchmark LLP signatures are shown to illustrate the potential of the upgraded detector. However, the potential of the upgraded triggerless readout has not been completely explored yet and its great flexibility could be exploited in several ways beyond those shown here.

5.2.2.1. Displaced di-leptons

The upgraded LHCb experiment is expected to have exceptional sensitivity to low-mass, displaced dilepton signatures thanks to the mass resolution, excellent vertexing, and the online selection allowed by the triggerless readout.

The upgrade LHCb sensitivity to dileptons has been explored in the literature in the context of dark photon searches. Two complementary signatures have been considered: an inclusive search for BSM gauge bosons (dark photons) in $A^{\prime} \to {\mu }^{+}{\mu }^{-}$, and a search for $A^{\prime}$ using radiative charm decays ${D}^{* 0}\to {D}^{0}A^{\prime} ,A^{\prime} \to {e}^{+}{e}^{-}$. The inclusive search [341] scans a large region from the dimuon threshold $2{m}_{\mu }$ all the way up to the Z pole. The second proposed signature [382] exploits a tag of the radiative decay of the ${D}^{* 0}$ using its reconstructed invariant mass and a di-electron dark photon final state to probe a much lower mass range allowed by the decay kinematics, $[2{m}_{e}$,142 MeV]. For both signatures, searches for both a prompt and a displaced dark photon vertex are carried out. The prompt search is expected to probe mixing parameters ² below 10⁻⁷ despite the large irreducible background from Drell–Yan and QCD¹⁸⁰ . Since the dark photons with masses above the η mass decay promptly for couplings that are accessible within LHCb, no attempt is made to probe displaced dark photons in that region.

An inclusive search for dark photons has already been performed with LHCb data collected in 2016 [269]. This was possible due to the high reconstruction and identification efficiency of soft di-muons at LHCb. These results demonstrated the unique sensitivity that can be reached at LHCb. The planned increase in luminosity and removal of the hardware-trigger stage in Run 3 should increase the number of expected $A^{\prime} \to \mu \mu$ decays in the low-mass region by a factor of ${ \mathcal O }$(100–1000) compared to the 2016 data sample. The limits placed by the current data and the sensitivity expected with future LHC runs is shown in figure 52.

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The exclusive search for ${D}^{* 0}\to {D}^{0}A^{\prime} ,A^{\prime} \to {e}^{+}{e}^{-}$ is much more challenging and not feasible prior to the upgrade, since the hardware trigger and the higher material budget degrade the sensitivity. This search highly relies on the online identification of ${e}^{+}{e}^{-}$ pairs, since over 5 trillion of these ${D}^{* 0}$ decays are expected in Run 3. The expected sensitivity probes unexplored regions of phase space at low $A^{\prime}$ mass and mixing ² that is usually in the realm of beam-dump experiments.

A displaced di-muon signature also appears in some HV scenarios [66], in which a hidden sector with strong dynamics showers and hadronizes into dark mesons that can have an appreciable decay rate to leptons. (For more information on dark showers, see chapter 7.) The upgraded LHCb prospects for this type of signature have been explored in [383] and are very promising. In the scenario explored therein, dark mesons are produced with large multiplicities of between 10 and 30. Selection criteria inspired by the proposed dark photon search [341] in the region after the first VELO module are applied. The expected reach for the proposed searches using Run 3 data from LHCb (15 $\,{\mathrm{fb}}^{-1}$) and from ATLAS/CMS (300 $\,{\mathrm{fb}}^{-1}$) are shown in figure 53. The model studied involves a 200 $\,\mathrm{GeV}$ $U(1)^{\prime}$ gauge boson Z_p decaying to a HV quark pair; showering and hadronization in the dark sector leads to a large multiplicity of hidden hadrons ω_V (with ${m}_{{\omega }_{V}}=0.3\,\mathrm{GeV}/{\text{}}{c}^{2}$) that can decay to di-muons. In this context, the upgraded LHCb detector could have better sensitivity than other proposed searches at ATLAS and CMS.

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5.2.2.2. Displaced jets

5.2.2.3. Displaced mesons

Quark–antiquark pairs from the decay of a low mass particle in the SM often hadronize into SM mesons that subsequently decay with known branching ratios. For example, a dark sector meson with a displaced decay to $c\bar{c}$ often produces two D mesons which in turn have non-negligible lifetimes. In this scenario, the authors of [383] have investigated the prospects of using more or less inclusive reconstruction of the two D meson decays at the upgraded LHCb. A similar approach could be used to target decays to $b\bar{b}$ that hadronize to B mesons since the latter is likely to produce D mesons in its decay. Since LHCb is designed to reconstruct heavy flavor decays, it can be competitive in this kind of search [383] (see figure 54). Furthermore, searches for displaced mesons will greatly profit from the software trigger, which is mainly designed to improve the efficiency of similar-looking hadronic decays of heavy flavor mesons.

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After a consolidation phase (Phase 1b) during long shutdown (LS) 3 aiming to run in the same conditions as in Phase 1a, the LHCb detector plans a Phase 2 upgrade during LS 4 (by 2030). The Phase 2 upgrade is needed to face even more challenging conditions than during previous runs. For example, particle multiplicity, PU, and radiation damage are expected to be ten times higher than those experienced in Phase 1. The LHCb experiment expects to collect at least 300 $\,{\mathrm{fb}}^{-1}$ by the end of Upgrade 2 [374].

Major improvements to the LHCb detector during Phases 1b and 2 that are relevant for LLP searches are described in the following, as well as some naïve projections of Run 1 results to an an integrated luminosity of 300 $\,{\mathrm{fb}}^{-1}$.

Magnet stations. Along with the 'long' and 'downstream' track types, 'upstream' tracks are also considered useful for LLP searches. These tracks correspond to soft charged particles bending out of the detector acceptance, produced from LLP candidates which decay within the VELO region. Aside from the installation of a new tracker during LS2, the Upstream Tracker, a proposal to add magnet stations inside the LHCb magnet to improve low momentum resolution is considered [384]. These magnet stations have been proposed to be installed for Phase 1b, and are foreseen to highly improve the tracking of low momentum particles produced from certain kind of LLP candidates, such as for example soft pions from 'disappearing' chargino tracks.

Material interactions. The presence of a VELO envelope at approximately 5 mm from the beam line in order to separate the VELO and the LHC vacuums, named 'RF-foil', strongly affects the background composition of LLP searches in the LHCb experiment. Namely, for LLP candidates decaying below 5 mm from the beam line, the main source of background is due to heavy flavour decays, while material interactions with the RF-foil compose the main background contribution for LLPs decaying above 5 mm from the beam line. While the former is purely due to QCD processes and hence not reducible, the latter is kept under control by the use of a detailed veto map (see [269]). However, the ideal case would be to completely remove the RF-foil during the Phase 2 upgrade [384], which would result in a large reduction of the background component due to material interactions. The improvements foreseen to the Phase 2 VELO (probably based on an updated version of the Phase 1 VELO), are expected to increase the sensitivity to shorter lifetimes and better PV and impact parameter resolution (see figure 55). Unfortunately, the removal of the RF-foil requires the development of new techniques to isolate the sensors from the beam radio frequency and is not necessarily seen as a viable option. Therefore, improving the material veto maps as much as possible by accurately modeling the material interactions would be desirable as a more realistic option for the HL-LHC era.

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Naïve Projections of Run 1 Results to the HL-LHC Era. By taking the published Run 1 results from the single displaced dijet search [253] at LHCb, a naïve extrapolation to the integrated luminosity foreseen to be recorded by LHCb during Phase 2, 300 $\,{\mathrm{fb}}^{-1}$, is presented in figure 56. These numbers have been obtained by simply scaling signal and background with the expected increase in cross section and luminosity, neglecting PU effects and expected detector improvements. The removal of neutral objects from jet reconstruction, and the use of machine-learning techniques are expected to assist in the required suppression of PU. Furthermore, jet substructure techniques are foreseen to improve the quality of di-jet object with lower mass.

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Despite a wide and seemingly comprehensive research program—both existing and, in this document, proposed to be expanded—for LLPs at the LHC, in cases of ultra-low-mass particles, ultra-long lifetimes, or unusual LLP charges, it is hard or impossible to trigger on and/or reconstruct such events in the main ATLAS, CMS, and LHCb detectors. This has led to new proposals for dedicated experiments to look for LLPs in new regimes that are otherwise inaccessible at the LHC. These experiments provide the best sensitivity to new millicharged LLPs, magnetic monopoles, and other LLPs arising from models such as those containing Higgs-portal hidden sectors, dark photons, and Majorana neutrinos.

As discussed in section 2.2, LLPs BSM are theoretically well motivated and come in wide range of masses and lifetimes. ATLAS and CMS have excellent sensitivity for fairly high mass LLPs, regardless of their lifetime (see, e.g. [4, 246, 386, 249]). Low mass and/or softer final states are more challenging due to both background and triggering limitations. In the short-lifetime regime, for cτ of the scale of the VELO, LHCb has sensitivity to somewhat lower masses and can trigger on softer muonic final states, generating complementary reach provided the LLP has a significant branching ratio to muons [253, 254, 279, 309, 387]. Finally, the low-mass/soft final states with rather long lifetimes are challenging for all three experiments. These signatures can be covered partially by NA62 [388] operating in beam dump mode, or by SHiP [389], or by dedicated LHC experiments like CODEX-b [104] (see section 5.3.5), FASER [105] (see section 5.3.6), or MATHUSLA [103] (see section 5.3.4). Each of these dedicated experiments is sensitive to different LLP lifetimes, masses, and production modes based on their position and orientation and thus each can be considered a necessary component of a comprehensive, coordinated search program for very long-lived particles at the LHC.

Monopole and exotics detector at the LHCoEDAL (MoEDAL) [101] ¹⁸⁰ is designed to search for manifestations of new physics through highly-ionising (HI) particles in a manner complementary to ATLAS and CMS [310]. The main motivation for the MoEDAL experiment is to pursue the quest for magnetic monopoles at LHC energies. Nonetheless the detector is also designed to search for any massive, long-lived, slow-moving particle [390, 391] with single or multiple electric charges arising in many scenarios of physics BSM [392].

The MoEDAL detector [311] is deployed around the intersection region at LHC Point 8 (IP8) in the LHCb VELO cavern. A schematic view of the MoEDAL experiment is shown in figure 57. It is a unique and largely passive detector comprising different detector technologies.

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The main sub-detector system is made of a large array of CR-39, Makrofol® and Lexan^TM nuclear track detector (NTD) stacks surrounding the intersection area. The passage of a HI particle through the plastic detector is marked by an invisible damage zone along the trajectory. The damage zone is revealed as a cone-shaped etch-pit when the plastic detector is chemically etched. Then the sheets of plastics are scanned looking for aligned etch pits in multiple sheets. The MoEDAL NTDs have a threshold of z/β ∼ 5, where z is the charge and β = v/c the velocity of the incident particle.

Another type of NTD installed is the very high charge catcher (z/β ∼ 50). It consists of two flexible low-mass stacks of Makrofol®, deployed in the LHCb acceptance between RICH1 and the Trigger Tracker. It is the only NTD (partly) covering the forward region, adding only ∼0.5% to the LHCb material budget while enhancing considerably the overall geometrical coverage of MoEDAL.

A unique feature of the MoEDAL detector is the use of paramagnetic magnetic-monopole trappers (MMTs) to capture magnetically-charged HI particles. The high magnetic charge of a monopole—being at least one Dirac charge g_D = 68.5e—implies a strong magnetic dipole moment, which may result in strong binding of the monopole with the nuclei of the aluminium MMTs. In such a case, the presence of a trapped monopole would be detected through the induction technique by measuring the persistent current, defined as the difference between the superconducting magnetometer currents before and after the passage of the MMT bar through the sensing coil [393, 394].

The only non-passive MoEDAL sub-detector is an array of TimePix pixel devices distributed throughout the MoEDAL cavern, forming a real-time radiation monitoring system of HI beam-related backgrounds. The operation in time-over-threshold mode allows a 3D mapping of the charge spreading in the volume of the silicon sensor, thus differentiating between various particles species from mixed radiation fields and measuring their energy deposition.

The MoEDAL detector is designed to fully exploit the energy-loss mechanisms of magnetically charged particles [395–398] in order to optimise its potential to discover these messengers of new physics. Multiple theoretical scenarios have been proposed over the years in which magnetic charge would be produced at the LHC [392], resulting in such possible new particles as light 't Hooft–Polyakov monopoles [397–399], electroweak monopoles [400–404], global monopoles [405–410], and monopolium [396, 411–413]. Magnetic monopoles that carry a non-zero magnetic charge and dyons possessing both magnetic and electric charge are predicted by many theories including grand-unified and superstring theories [414–416].

A possible explanation for the non-observation of monopoles so far is Dirac's proposal [395, 396, 411] that monopoles are not seen freely because they form a bound state called monopolium [412, 413, 417, 418] being confined by strong magnetic forces. Monopolium is a neutral state, difficult to detect directly at a collider detector, although its decay into two photons would give a rather clear signal for ATLAS and CMS [419]. Nevertheless the LHC radiation detector systems can be used to detect final-state protons ${pp}\to {pXp}$ exiting the LHC beam vacuum chamber at locations determined by their fractional momentum losses [420]. Such a technique would be appealing for detecting monopolia.

The MoEDAL detector is also designed to search for any massive, long-lived, slow-moving particles [390, 391] with single or multiple electric charges arising in many scenarios of physics BSM. Supersymmetric LLPs [421], quirks, strangelets, Q-balls, and many others fall into this category [392]. A generic search for high-electric-charge objects is currently underway.

For the 2016 run at 13 TeV, the MMT included 672 aluminium rods (for a total mass of 222 kg) that were placed 1.62 m from the IP8 LHC IP under the beam pipe on the side opposite to the LHCb detector. The MMT bars were analysed and no magnetic charge $\gt \,0.5{g}_{{\rm{D}}}$ was detected in any of the exposed samples when passed through the ETH Zurich SQUID, which is a DC SQUID long-core magnetometer [422]. Hence cross section limits are obtained for Drell–Yan pair production of spin-1, spin-1/2 and spin-0monopoles for $1{g}_{{\rm{D}}}\leqslant | g| \leqslant 5{g}_{{\rm{D}}}$ at 13 TeV [422] improving previous bounds set by MoEDAL at 8 TeV [311] and 13 TeV [423]. Monopole production via photon fusion is also now considered in MoEDAL monopole search analyses [424] following recent studies [425]. However, the large monopole-photon coupling invalidates any perturbative treatment of the cross section calculation and hence any result based on the latter is only indicative. This situation may be resolved if thermal production in heavy-ion collisions—that does not rely on perturbation theory—is considered [426], or by including a magnetic-moment term in monopoles with spin [425].

To recapitulate, under the assumption of Drell–Yan cross sections, MoEDAL has derived mass limits for $1{g}_{{\rm{D}}}\leqslant | g| \leqslant 5{g}_{{\rm{D}}}$, complementing ATLAS results [215, 427], which placed limits for monopoles with magnetic charge $| g| \leqslant 1.5{g}_{{\rm{D}}}$, as shown in figure 58. The ATLAS bounds are better that the MoEDAL ones for $| g| =1{g}_{{\rm{D}}}$ due to the higher luminosity delivered in ATLAS and the loss of acceptance in MoEDAL for small magnetic charges. On the other hand, higher charges are difficult to be probed in ATLAS due to the limitations of the level-1 trigger deployed for such searches. Limits on production cross sections of singly-charged magnetic monopoles set by various colliders are presented in [414, 415], while general limits including searches in cosmic radiation are reviewed in [428].

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MoEDAL is proposing to deploy the MoEDAL apparatus for detecting penetrating particles (MAPP) in a tunnel shielded by some 30–50 m of rock and concrete from the IP8 [430, 431]. A prototype of the MAPP detector was installed in 2017. It is envisaged that the full detector will be installed in LS2 to take data in LHC Run 3. The purpose of the detector is to search for particles with fractional charge as small as one-thousandth the charge of an electron. This detector would also be sensitive to neutral particles from new physics scenarios via their interaction or decay in flight in the ∼10 m decay zone in front of the detector or in the detector itself. The isolation of the detector means that the huge background from SM processes in the main detectors is largely absent. Also, the detector can be placed at various angles to the beam axis (from 5° to 25°). The ability to vary depth and angle enhances MoEDAL to be able to distinguish between theoretical scenarios in the event a signal is observed.

The first apparatus specifically designed to detect mini-charged particles was the Stanford Linear Accelerator Centre (SLAC) 'beam dump'-type detector, comprising scintillator bars read out by photomultiplier tubes [432]. MoEDAL's new detector, shown in figure 59, and milliQan (discussed above in section 5.3.3) proposed for deployment near to the CMS detector [102] also designed to search for mCPs, both have a design that harks back to the original SLAC detector. In order to reduce backgrounds from natural radiation the photomultiplier tubes and scintillator detectors of the MoEDAL apparatus will be constructed from materials with low natural backgrounds currently utilised in the astroparticle-physics arena. Its calibration system utilises neutral density filters to reduce the received light of high incident muons that manage to penetrate to the sheltered detector from the IP, in order to mimic the much lower light levels expected from particles with fractional charges.

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MoEDAL is also planning another new sub-detector called MALL (MoEDAL apparatus for detecting extremely long lived particles) [431]. In this case MoEDAL trapping volumes, after they have been scanned through the ETH Zurich SQUID facility to identify any trapped monopole will be shipped to a remote underground facility to be monitored for the decay of pseudo-stable massive charged particles that may also have become trapped. MALL is the detector that monitors MoEDAL trapping volumes for decays of captured particles. It is envisaged that MALL will be installed deep underground at SNOLAB in Canada where cosmic backgrounds are minimised to one muon per 0.27 m² d⁻¹. Background is further reduced by the ability to determine if a detected track originated within the monitored volume and also by energy cuts on deposited signals. A schematic view of the detector is shown in figure 60. Initial estimates indicate that lifetimes up to around 10 years can be probed. The MALL detector is designed to be sensitive to charged particles and to photons, with energy as small as 1 GeV. It is envisaged that construction of the detector will begin after the MAPP detector is full deployed.

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The possibility of analysing decommissioned parts of the LHC beam-pipe system at the ATLAS, CMS and LHCb/MoEDAL sites with a SQUID to search for trapped magnetic monopoles has been proposed [433]. In this context the MoEDAL experiment may serve as a formal platform for coordinating machining, scanning and analysis work, in collaboration with interested ATLAS, CMS and LHCb members.

The induction technique has been successfully employed at the LHC with the dedicated MoEDAL trapping detector. Additional searches for trapped monopoles in beam pipe material would access wide windows of magnetic charges and production cross sections to which other LHC experiments are insensitive. The decommissioned central beryllium beam pipe sections of ATLAS and CMS, with a 4π coverage and exposure to the highest rates of 7 and 8 TeV pp collisions, are by far the most attractive samples to be analysed. The analysis on the CMS beam pipe is expected to be carried out in 2019.

MilliQan is a dedicated experiment at the LHC to search for mCP [102, 434]. The milliQan experiment is part of a general program to search for hidden sectors [435] and other BSM scenarios [436]. As an illustrative example, we show the sensitivity of milliQan to an extra Abelian gauge field coupled to a massive Dirac fermion ('dark QED') that mixes with hypercharge through the kinetic term [122]. The result is that the new matter field is charged under hypercharge with a fractional electric charge of , where $\epsilon \ll 1$. The milliQan experiment targets an unexplored part of the parameter space, namely mCP masses $0.1\lesssim {M}_{\mathrm{mCP}}\lesssim 100\,\mathrm{GeV}$, for charges Q at the ${10}^{-3}\,e-{10}^{-1}\,e$ level.

The experimental apparatus consists of three scintillator detector layers of roughly 1 m³ each, positioned near one of the high-luminosity IPs of the LHC. The experimental signature consists of a few photo-electrons (PE) arising from the small ionization produced by the mCPs that travel unimpeded through material after escaping the LHC detectors.

The milliQan experiment is planned to be sited in the PX56 Observation and Drainage gallery above the CMS underground experimental cavern. The proposed gallery is limited in space. The detector will be located in this tunnel at an optimized location that is 33 m from the CMS IP, behind 17 m of rock, and at an angle of 43.1 degrees from the horizontal plane. The selected location in a 3D model is shown in figure 61.

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The milliQan detector is a $1\,{\rm{m}}\times 1\,{\rm{m}}\times 3\,{\rm{m}}$ plastic scintillator array. The array will be oriented such that the long axis points at the nominal CMS IP. The array is subdivided into 3 sections each containing 400 $5\,\mathrm{cm}\times 5\,\mathrm{cm}\times 80\,\mathrm{cm}$ scintillator bars optically coupled to high-gain photomultiplier tubes (PMTs). The detector will be shielded from other background sources such as activity in the scintillator and environmental radiation. With an estimated detection efficiency of about 10%, milliQan expects an average of ${ \mathcal O }(1)$ PE from each attached phototube for each mCP with $Q={ \mathcal O }({10}^{-3})\,e$ that traverses 80 cm of plastic scintillator. The signal is a longitudinal triple-incidence of hits with one or more PEs; a triple-incidence within a 15 ns time window along longitudinally contiguous bars in each of the three sections is required to reduce the background from dark-current noise. Requiring triple-incidence is expected to control background to ${ \mathcal O }(10)$ events per year with ${N}_{\mathrm{PE}}\geqslant 1$. The milliQan detector will self-trigger to a dedicated readout with no dead time from readout, up to rates of ∼1 kHz. Energy calibration will be done in situ using an ²⁴¹Am source.

The dominant background is expected to come from dark-current pulses in the PMTs. Pulses from background radiation, including cosmic muons, will consist of 1000s of PEs that can be easily vetoed offline. Assuming a total background rate per PMT of ν_B = 500 Hz, with a time window of (Δt)_online = 100 ns, milliQan expects a double coincident trigger rate per board of 1.5 Hz. The entire detector will be read out if one board triggers and there will be 50 such boards in total. Therefore, the full background trigger rate is expected to be 75 Hz. Offline, the time window will be tightened to (Δt)_offline = 15 ns, yielding an offline background rate for a triple coincidence of 2.8 × 10⁻⁸ Hz. Since there are 400 such sets, the total offline background rate is estimated to be 1.1 × 10⁻⁵ Hz. With these background rates, milliQan estimates a total of 165 (330) background events in 300 (3000) fb⁻¹ of integrated luminosity.

The milliQan collaboration has performed a full simulation of the experiment to evaluate the projected sensitivity to various mCP electric charges and masses. The simulation is performed in two stages. In the first, the production of mCP particles via Drell–Yan , J/Ψ, ϒ(1S), ϒ(2S), and ϒ(3S) channels at a center-of-mass energy of 14 TeV is performed. Particles produced at the IP are propagated to the proposed experimental site described above using a map of the CMS magnetic field. The effects of multiple scattering and energy loss are included using a simplified model of the CMS detector material budget and a region of rock spanning 17 m between the CMS experimental cavern and the proposed experimental site. The number of expected mCP particles per fb⁻¹ of integrated luminosity incident at the detector is computed as a function of the mass of the mCP. The signal efficiency is then estimated after processing the calculated particles as they would emerge from the IP through a full Geant4 simulation of the detector; this is necessary because the small charge regime is sensitive to details such as the reflectivity, the light attenuation length, and the shape of the scintillator. These details, as well as the quantum efficiency, light-emission spectrum and the fast-time constants were modeled in Geant4 using the specifications provided by the manufacturers for the scintillator and PMTs. Combining the estimated background rates discussed above with the cross sections, acceptances and efficiencies calculated for all masses and electric charges, the sensitivity projections of the milliQan experiment for LHC and HL-LHC are shown in figure 62.

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A 1/100 scale 'demonstrator' of milliQan to validate the detector concept was installed in the PX56 location at CERN during Technical Stop 2 of 2017 and was upgraded during the 2017–2018 year-end technical stop. This demonstrator, shown in figure 63, has been recording data since its installation, and expects to have first results later this year. If funding is secured, construction of the full milliQan apparatus is planned for 2019, with installation in the tunnel in 2020.

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The basic motivation for the MAssive Timing Hodoscope for Ultra-Stable neutraL pArticles (MATHUSLA) detector [103] is the search for LLPs with lifetimes much greater than the size of the LHC main detectors, cτ ≫ 100 m. Any detector that can be reasonably constructed could only catch a small fraction of such LLPs decaying inside of its volume. Even with potentially large LLP production rates at the LHC, suppression of backgrounds is therefore crucial for discovery.

For LLP searches with high-energy or lepton-containing final states, the spectacular nature of displaced-vertex (DV) signals leads to very low backgrounds in searches at LHC detectors such as ATLAS or CMS. Any other class of LLP signature suffers from backgrounds and triggering limitations that can be significant. This greatly curtails the main detectors' ability to discover LLPs with very long lifetimes.

To address this broad blind spot of existing detectors, MATHUSLA is proposed to be a large, relatively simple surface detector that can robustly reconstruct DVs with good timing resolution. This gives MATHUSLA a similar geometric acceptance to LLP decays in the long-lifetime limit as the main detectors, while providing shielding from QCD backgrounds and sufficient tracking to reject ubiquitous CRs. As a result, MATHUSLA is able to detect LLPs produced with ∼1 pb cross sections at the HL-LHC with lifetimes near lifetimes of ∼0.1 s, which is generally the limit imposed by big-bang nucleosynthesis (BBN).

The simplified detector design for MATHUSLA is shown in figure 64. The main component of the detector is a tracker array situated above an air-filled decay volume that is 20 m tall and 200 m × 200 m in area. The tracker should have on the order of five planes to provide robust tracking with ∼ ns timing and ∼ cm spatial resolution. The current MATHUSLA design employs proven and relatively cheap technologies to allow for MATHUSLA's construction in time for the HL-LHC upgrade. Therefore, the trackers are envisioned to be implemented with resistive plate chambers (RPCs), which have been used for very large area experiments in the past [437, 438], while plastic scintillators provide the surrounding veto.

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This minimal design has been shown to be capable of measuring the LLP boost on an event-by-event basis [439] using the geometry of the LLP visible decay products. Final-state multiplicity provides a straightforward discriminant between hadronic and electromagnetic decays. Additional particle identification capability, as well as detection of final-state photons, might be possible by inserting an additional material layer between tracking layers to induce an electromagnetic shower that can be used to distinguish electrons, photons and muons.

As argued in [103], MATHUSLA could search for LLPs decaying into charged particles with little or no backgrounds. In figure 64 is shown, schematically, the two main MATHUSLA signals, LLPs decaying into at least two charged leptons, or into jets that contain ${ \mathcal O }(10)$ charged hadrons [439]. In 50%–90% of leptonic decays and practically 100% of hadronic decays [439], two or more charged partices hit the ceiling due to the LLP boost and are recorded by the tracker. The charged particle trajectories can be fitted to reconstruct a DV. Unlike most analyses in the main detectors, these DVs must satisfy the additional stringent requirement that all trajectories coincide in time at the DV. The scintillator is used as a veto to ensure that the charged particles originate at the DV: there can be no hits along the line between the vertex and the LHC main IP, nor along the lines obtained by extrapolating the individual charged particle trajectories backwards. These exhaustive geometric and timing requirements make it extremely difficult for backgrounds to fake the LLP signal. Cosmic rays can be rejected since they travel in the wrong direction (as well as occurring mostly in CR showers with extremely highly correlated particle multiplicity in the detector). Muons from the LHC collision do not satisfy the DV signal requirement. The rare occasions in which muons scatter inside the decay volume can be vetoed with the scintillators. Finally, neutrinos from CRs and LHC collisions can scatter in the decay volume and produce DV, but those can also be rejected with geometric and timing requirements. We refer the reader to [103] for more details. More comprehensive studies of these backgrounds and their rejection strategies, including full simulations, are currently in progress.

An important general class of signals are LLPs with masses $\lesssim \,100\,\mathrm{GeV}$ that decay hadronically and are produced without other highly visible signals like high MET or high-energy leptons. MATHULSLA can improve the sensitivity to these LLP production cross sections by a factor of ∼ 10³ compared to searches with the main detectors alone. This is illustrated in figure 65, which shows MATHUSLA's sensitivity to hadronically decaying LLPs produced in exotic Higgs decays [103] compared to an optimistic projection for searches for a single DV in the ATLAS MS [262]. For branching ratios of ∼ 10%, the BBN lifetime limit [440] can be probed.

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Apart from reaching the BBN upper limit or ceiling of LLP parameter space, MATHUSLA extends the power of other LHC measurements. If a ∼ 10% invisible branching ratio for the Higgs was detected via coupling measurements at the HL-LHC, the absence of a MATHUSLA signal would lend strong support to the interpretation that the Higgs decayed to a stable component of DM.

Beyond LLPs produced in rare Higgs decays, MATHUSLA is a general-purpose LLP detector that is sensitive to a wide range of other models. Its reach for other BSM scenarios has been explored in [172, 174, 198, 441–447]. The general physics case for MATHUSLA's construction is made systematically in the recently released whitepaper [2].

It is important to point out that MATHUSLA is a very flexible detector concept that is completely scalable. The sensitivity of MATHUSLA is roughly proportional to the decay volume (which scales with surface area) and roughly independent of the precise geometry or location of the detector, as long as it is ${ \mathcal O }(100\,{\rm{m}})$ horizontally displaced from the IP. Therefore, a detector with smaller or larger volume than the benchmark in figure 64 may be implemented, depending on available space and budget. Furthermore, the detector volume can be divided into smaller, independent modules (which cooperate for triggering purposes). These can be mass-produced economically and arranged according to the requirements of the experimental site. Such a modular construction also allows for a natural way to improve or extend the physics program of the experiment in an efficient way, by eventually upgrading, for example, one or a few modules with additional capabilities, such as higher tracking resolution for reconstruction of very low-mass LLPs below 10 MeV, or an additional material layer between the trackers for particle ID.

The MATHUSLA collaboration is currently studying such a modular design with the aim of producing a Letter-of-Intent in 2018. Crucial to this endeavor is the data from the MATHUSLA test stand, a ∼ 3 × 3 × 5 m MATHUSLA-type detector that took a few days of data in the ATLAS instrument hall in 2017 and will take data for a few months in 2018. This allows local CR backgrounds to be measured, background rejection and signal reconstruction strategies to be tested, and simulation frameworks to be calibrated.

In conclusion, the MATHUSLA detector concept calls for a dedicated LLP surface detector above ATLAS or CMS. A detector volume of ∼10⁶ m³ gives sensitivity to LLPs near the BBN lifetime limit if they are produced with ∼pb cross section. This improves LLP sensitivity, compared to the main detectors alone, by several orders of magnitude for many LLP scenarios. The detector is simple and relies on proven technology, making its construction in time for the HL-LHC upgrade feasible. Once constructed, MATHUSLA could function without modification as a detector for the HE-LHC (with increased sensitivity). A small-scale test stand detector is already taking data at CERN, and studies are underway to finalize a detailed design for the full-scale detector.

The CODEX-b proposal involves housing a small detector in the LHCb cavern—external to the LHCb detector itself—in a space approximately 25 m from the interaction point (IP8), behind the 3 m thick concrete UXA shield wall. This space is presently occupied by the LHCb data acquisition (DAQ) system, but will become available before Run 3 once the DAQ system is relocated to the surface. The layout of the cavern is shown in figure 66, with the location of CODEX-b overlaid. The nominal CODEX-b configuration features a 10 × 10 × 10 m volume instrumented with RPC tracking layers or other off-the-shelf tracking technology, as well as roughly 25 interaction lengths of shielding near IP8—e.g. 4.5 m of Pb—to suppress primary and secondary ${K}_{L}$, neutron, and other hadronic backgrounds. This shield requires an active muon veto with an efficiency of ${ \mathcal O }({10}^{-5})$, in order to reject backgrounds induced by muons or other charged particles in the downstream parts of the shield. The veto is located several metres within the shield such that backgrounds induced by neutral particles remain suppressed. See [104] for a study of a proof-of-concept example detector layout and corresponding tracking efficiency, as well as a detailed study of the backgrounds. More ambitious technologies, including calorimetry, precision TOF measurements, or integration into the LHCb readout may also be feasible.

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For the current discussion, the reach of CODEX-b for two benchmark models is quantified: first, a light scalar field, $\varphi$, that mixes with the SM Higgs boson is considered. If ${m}_{\varphi }\lesssim 5\,\mathrm{GeV}$, the production mode is primarily through inclusive $b\to s\varphi$ decays [449–451]. The LLP $\varphi$ subsequently decays back to SM fermions through the same Higgs portal. The reach in terms of ${m}_{\varphi }$ and the mixing angle ${s}_{\theta }$ is shown in the left-hand panel of figure 67. CODEX-b significantly extends the projected reach of LHCb using only VELO-based DV reconstruction, and covers part of the parameter space to which SHiP [452] and MATHUSLA [443] are projected to be sensitive. Studies of the potential LHCb reach to longer lifetimes using downstream tracking are ongoing [378, 453]. The right-hand panel of figure 67 indicates the reach for more general models, where the lifetime and production rate of $\varphi$ are unrelated.

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For the second benchmark, a dark boson, ${\gamma }_{{\rm{d}}}$, produced through the exotic Higgs decay $h\to {\gamma }_{{\rm{d}}}{\gamma }_{{\rm{d}}}$ is considered. For concreteness the ${\gamma }_{{\rm{d}}}$ is taken to be a spin-1 field which can decay through mixing with the SM photon [70, 230, 456, 457]. In this benchmark, the production and decay are therefore controlled by different portals. The projected reach is shown in figure 68, overlaid with the reach of ATLAS [262, 273] and MATHUSLA [103]. In particular, at low γ_d masses, CODEX-b complements and significantly extends the reach of ATLAS and CMS.

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Finally, it might be possible to install a larger version of the CODEX-b detector at IP2, after the ALICE collaboration concludes its heavy ion program. This option is named 'A Laboratory for Long-Lived eXotics' (AL3X) [459], and can make use of the existing ALICE TPC, supplemented with a thick hadron absorber. The B-field from the L3 magnet would provide a good momentum measurement of the tracks, something which is absent in MATHUSLA and CODEX-b. The feasibility of this proposal is however contingent upon a luminosity upgrade of IP2, as well as the possible continuation of the ALICE physics during Run 5.

If new LLPs are light compared to the weak scale and very weakly coupled, the focus at the LHC on searches for new particles at high ${p}_{{\rm{T}}}$ may be completely misguided. In contrast to TeV-scale particles, which are produced more or less isotropically, light particles with masses in the MeV–GeV range are dominantly produced at low ${p}_{{\rm{T}}}$. In addition, because the new particles are extremely weakly coupled, very large SM event rates are required to discover the rare new physics events. These rates are not available at high ${p}_{{\rm{T}}}$, but they are available at low ${p}_{{\rm{T}}}$: at the 13 TeV LHC, the total inelastic pp scattering cross section is ${\sigma }_{\mathrm{inel}}(13\,\mathrm{TeV})\approx 75\,\mathrm{mb}$ [460, 461], with most of it in the very forward direction. This implies

$$\begin{eqnarray}&&{N}_{\mathrm{inel}}\approx 2.3\,\times \,{10}^{16}\ (2.3\times {10}^{17})\end{eqnarray} \tag{ 5.5 }$$

inelastic pp scattering events for an integrated luminosity of 300 fb⁻¹ at the LHC ($3\,{\mathrm{ab}}^{-1}$ at the HL-LHC). Even extremely weakly-coupled new particles may therefore be produced in sufficient numbers in the very forward region. Due to their weak coupling to the SM, such particles are typically long lived and travel a macroscopic distance before decaying back into SM particles. Moreover, such particles may be highly collimated. For example, new particles that are produced in pion (B-meson) decays are typically produced within angles of $\theta \sim {{\rm{\Lambda }}}_{\mathrm{QCD}}/E$ (${m}_{B}/E$) off the beam-collision axis, where E is the energy of the particle. For E ∼ TeV, this implies that even ∼ 500 m downstream, such particles will have only spread out ∼ 10 cm–1 m in the transverse plane. A small and inexpensive detector placed in the very forward region may therefore be capable of extremely sensitive searches to LLPs, provided a suitable location can be found and the signal can be differentiated from the SM background.

Forward search experiment (FASER) [105, 462–465], the is an experiment designed to take advantage of this opportunity. It is a small detector, with volume ∼ 1 m³, that is proposed to be placed along the beam-collision axis, several hundreds of meters downstream from the ATLAS or CMS IP. In the following, we present a promising location of FASER, discuss the properties of the signal and the required detector design, and present the new physics reach for representative models.

As shown in figure 69, FASER will be placed along the beam collision axis, several hundreds of meters downstream from the ATLAS or CMS IP after the LHC tunnel starts to curve. A particularly promising location is a few meters outside the main LHC tunnel, 480 m downstream from the ATLAS IP, in service tunnel TI12, as shown in the bottom panels of figure 69. (A symmetric location on the other side of ATLAS in tunnel TI18 is also possible.) This tunnel was formerly used to connect the SPS to the LEP tunnel, but is currently empty and unused. As shown on the tunnel map in the lower left panel of figure 69, the beam collision axis passes through TI12 close to where it merges with the main LHC tunnel. A more detailed study of the intersection between the beam collision axis and TI12 verifies that there exists space for FASER in the tunnel, as shown in the lower-right panel of figure 69.

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In this location, FASER harnesses the enormous, previously completely unused and unexamined cross section for very forward physics ($\sigma \sim 100\ \mathrm{mb}$). This cross section implies that even very weakly coupled new particles can be produced in large numbers at the LHC. In addition, the production of LLPs at high center-of-mass energy results in long average propagation distances ($\bar{d}\sim { \mathcal O }(100)\,{\rm{m}}$) and decays that are far beyond the main LHC infrastructure in regions where the backgrounds are expected to be negligible.

FASER will search for LLPs that are produced at or close to the ATLAS IP in the very-forward direction, travel approximately 480 m, and then decay via $\mathrm{LLP}\to \mathrm{charged}\ \mathrm{tracks}+X$. When LLPs are produced in the very-forward region of the beam collision axis, they typically have very high energies E  ∼  TeV. Although the identity of the LLP decay products depends on the mass of the LLP and the concrete new-physics model, some of the standard, characteristic LLP decay signatures are generically expected, such as two or more stable charged particles, such as electrons, muons or pions. This leads to a striking signature at FASER: two oppositely charged tracks with very high energy that emanate from a vertex inside the detector and which have a combined momentum that points back to the IP. A measurement of individual tracks with sufficient resolution and an identification of their charges is therefore imperative if the apparatus is to make use of kinematic features to distinguish signal from background. A tracking-based technology, supplemented by a magnet and a calorimeter to allow for energy measurements, will be the key components of FASER. Details of the detector design can be found in the Letter of Intent [462] and Technical Proposal [464].

The FASER signals consist of two extremely energetic (∼TeV) coincident tracks or photons starting at a common vertex and pointing back to the ATLAS IP. Muons and neutrinos are the only known particles that can transport such energies through 100 m of rock and concrete between the IP and FASER. The CERN Sources, Targets, and Interactions group has computed the fluxes of muons and neutrinos at the FASER location using a FLUKA simulation [466–468]. These muon fluxes then allow one to estimate the rate and energy spectrum of muon-associated radiative processes near the detector. Preliminary estimates show that muon-associated radiative processes and neutrino-induced backgrounds may be reduced to negligible levels [464, 464].

Emulsion detectors and battery-operated radiation monitors were installed in both TI12 and TI18 during Technical Stops in 2018. The results from these in situ measurements have validated the estimates of the FLUKA simulation, confirming that the high-energy particle background is highly suppressed and radiation levels are also very low and not expected to be problematic for detector electronics. Additional work is ongoing to refine background estimates, evaluate signal efficiencies, and optimize the detector.

In its first stage, FASER is an extremely compact detector, sensitive to decays in a cylindrical region of radius R = 10 cm and length L = 1.5 m. FASER is planned to be constructed and installed in LS 2 and will collect data during Run 3 of the 14 TeV LHC (2021–23). After FASER's successful operation, FASER 2, a much larger successor with roughly R ∼ 1 m and L ∼ 5 m, could be constructed in LS 3 and collect data during the HL-LHC era (2026–35). More details on the FASER timeline can be found in the Letter of Intent [462] and Technical Proposal [464].

The sensitivity of FASER to detect LLPs has been studied in a plethora of new physics models, including dark photons [105], dark Higgs bosons [469], HNLs [297], axion-like particles (ALPs) [470], iDM [471], flavor-specific scalar mediators [472], $U{(1)}_{B-L}$-gauge bosons [473], R-parity violating supersymmetry [60, 174] and SIMPs [474]. A summary on FASER's physics reach for LLP can be found in [463]. Combined, these studies establish FASER's significant impact on the LHC's discovery reach for LLPs. The physics reach at FASER and FASER 2 for these models is shown in figure 70. Here we assume that backgrounds can be reduced to negligible levels. The gray-shaded regions of parameter space have already been excluded by previous experiments. For comparison we also show the projected reaches of other proposed experiments that search for LLPs.

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Dark photons and ALPs (upper panels) are mainly produced in the decay of light mesons, via dark bremsstrahlung, or through the Primakoff process, and they are therefore very collimated around the beam collision axis. Already a very small detector is able to probe large and unconstrained regions of parameter space, making dark photons an ideal short-term goal for FASER. In contrast, dark Higgs bosons and HNLs (lower panels) define good long-term physics goals. They are both mainly produced in heavy meson decays, leading to a larger spread around the beam collision axis. A larger, but still relatively small, detector with R ∼ 1 m is then required to exploit the full potential of FASER.

The interpretation of experimental results using simplified models typically corresponds to producing upper limits on the production cross section or signal efficiencies for a specific SMS topology (production and decay channel). These results are provided as a function of the simplified model parameters, which have been largely taken to be the masses of the BSM particles appearing in the topology. For LLP topologies, however, a new parameter must be considered: the LLP lifetime (see chapter 2). With the exception of searches for stable particles, the lifetime is one of the main parameters affecting the topology efficiency and upper limit.

Once signal efficiencies¹⁸⁸ () are provided for one or more SMS topologies, these can be used, under some approximations, to quickly compute the number of expected signal events (S) for a full model:

$$\begin{eqnarray}&&S={ \mathcal L }\times \left(\displaystyle \sum _{\mathrm{SMS}}{\sigma }_{\mathrm{SMS}}\times {\mathrm{BR}}_{\mathrm{SMS}}\times {\epsilon }_{\mathrm{SMS}}\right),\end{eqnarray} \tag{ 6.1 }$$

where ${ \mathcal L }$ is the luminosity for the respective search and the sum runs over simplified model topologies. Since the production cross section (${\sigma }_{\mathrm{SMS}}$) and branching ratios (${\mathrm{BR}}_{\mathrm{SMS}}$) for each topology can be quickly computed for any full model, the simplified model signal efficiencies (${\epsilon }_{\mathrm{SMS}}$) can be directly used to obtain the signal yield. This procedure does not rely on any MC simulation or recasting of LLP searches and can be easily applied to a wide variety of models, provided ${\epsilon }_{\mathrm{SMS}}$ is known. The main limitation of this approach comes from the limited (although growing) number of SMS results available. Since ${\epsilon }_{\mathrm{SMS}}$ is typically known only for very few simplified models, the sum in equation (6.1) is limited to the number of available topologies, resulting in an under-estimation of S.

For prompt SUSY searches, a systematic approach for reinterpreting simplified model results based on the procedure outlined above has been developed in [482, 485]. Furthermore, using the large number of available SUSY SMS results, public tools are available for constraining full models using these results [483, 485]. The same procedure can also be applied to LLP SMS results, as shown in [97] for the case of HSCPs and implemented recently in SModelS [493]. In the next section we review some of the results found in [97]. Although these have been obtained within the context of HSCPs, the main results can be generalized to other LLP signatures, and demonstrate some of the advantages and shortcomings of reinterpretations using LLP simplified models.

The CMS search for HSCPs in [495] provided signal efficiencies for the simplified model topology ${pp}\to \tilde{\tau }\tilde{\tau }$ as a function of the stau mass. In the language of the simplified models of section 2.4.2, this is the direct pair production mode of a charged LLP. The stau is assumed to be stable (at detector scales), thus producing a highly ionizing track, which can be used to search for this scenario (see section 3.5). Since the stau lifetime (τ) is assumed to be ≫ 10 ns, the signal efficiencies do not depend on τ, thus simplifying the SMS parameter space, which reduces to the stau mass¹⁸⁹ . The relevant selection efficiencies required for a general purpose MC recasting of the HSCP search have also been provided by the CMS analysis; see section 6.4.1 for details.

The efficiencies for the stau simplified model can be used to constrain a full BSM scenario which contains HSCPs. In [97], the region of the CMSSM parameter space with ${m}_{\tilde{\tau }}-{m}_{{\tilde{\chi }}_{1}^{0}}\lt {m}_{\tau }$ has been considered, since it provides a possible solution to the Lithium problem [499, 500]. Due to the small mass difference, the stau is long-lived and decays outside the detector, thus generating a HSCP signal. In figure 73, we show the constraint on the CMSSM parameter space obtained using only the simplified model provided by CMS (direct stau production). Since the simplified model only contains one parameter, it translates to a limit on the stau mass (${m}_{\tilde{\tau }}\lt 260$ GeV), as shown by the blue region in figure 73. In this CMSSM scenario, however, direct production of staus only contributes to a small fraction of the total HSCP signal, since staus are typically produced from cascade decays of heavier SUSY states, such as charginos, squarks and gluinos. (Note that these correspond to the HP modes of section 2.4.2.) Furthermore, there are several possible topologies which contain a stau and the LSP (${\tilde{\chi }}_{1}^{0}$) in the final state, thus resulting in a mixed missing energy-HSCP signature. Therefore using only the CMS constraints for the direct stau production simplified model largely underestimates the sensitivity of the CMS search.

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In order to improve the constraints shown in figure 73, one must have efficiencies for several SMS topologies. Fortunately, a MC recasting of the 8 TeV CMS search is possible (see section 6.4.1 for details) and can be used to compute simplified model efficiencies. In [97], seven additional simplified models containing cascade decays were considered and their efficiencies computed as a function of the masses appearing in the topology. A summary of the topologies considered are shown in table 5. It is important to point out that it is not necessary to specify the SM final states appearing in the simplified models, since the HSCP search is inclusive and the efficiencies do not depend on the additional event activity. Using this extended database of simplified model efficiencies and equation (6.1), we can compute a more inclusive signal yield for each point of the CMSSM parameter space and improve the constraints on the model. The results are shown in figure 74, where we see a drastic improvement in the region excluded by the constraints on HSCPs, as expected. For this specific scenario (with $\tan \beta =10$), all the parameter space is excluded either by the CMS or DM constraints [97].

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Table 5.  Definitions of the HSCP simplified models considered in this section. The symbol X represents the HSCP, Y_i represents intermediate BSM particles, SM represents any Standard Model particle and inv represents an invisible final state, such as the neutralino. The correspondance with the simplified models language of chapter 2 (section 2.3.1) is also given.

SMS topology	Notation in chapter 2
${pp}\to X\,X$	DPP
${pp}\to {Y}_{1}\,{Y}_{1},{Y}_{1}\,\to \mathrm{SM}\,X$	HP
${pp}\to {Y}_{1}\,{Y}_{1},{Y}_{1}\,\to \mathrm{SM}\,{Y}_{2},{Y}_{2}\,\to \mathrm{SM}\,X$	—
${pp}\to {Y}_{1}\,{Y}_{2},{Y}_{1}\,\to \mathrm{SM}\,{Y}_{2},{Y}_{2}\,\to \mathrm{SM}\,X$	—
${pp}\to Y\,Y,Y\,\to \mathrm{SM}\,\mathrm{SM}\,X$	HP
${pp}\to \mathrm{inv}\,X$	CC
${pp}\to {Y}_{1}\,{Y}_{2},{Y}_{1}\,\to \mathrm{SM}\,\mathrm{inv},{Y}_{2}\,\to \mathrm{SM}\,X$	—
${pp}\to {Y}_{1}\,{Y}_{2},{Y}_{1}\,\to \mathrm{SM}\,\mathrm{inv},{Y}_{2}\,\to {Y}_{3}\,\mathrm{SM},{Y}_{3}\,\to \mathrm{SM}\,X$	—

Figure 74 illustrates the feasibility of using simplified model efficiencies to constrain full models. This approach has the advantage of being computationally inexpensive (once the efficiencies are known) and can be used to quickly test a large number of model points. However the approach relies on a few approximations and is never fully inclusive, since the number of SMS topologies with published efficiencies is always limited. Hence, it is important to verify how close the simplified model reinterpretation comes to the full recasting using a MC simulation. In [97] it was shown that, within the CMSSM scenario discussed above and using eight simplified model topologies, the SMS results reproduce the full simulation within 20% or better. Since this error is of the order of the uncertainties in recasting, the use of simplified models becomes a viable alternative to full recasting. The SMS reinterpretation is even more relevant for the cases where a straightforward MC recasting is not possible.

Lessons learned. The example discussed in section 6.3.2 illustrates how simplified models for LLPs can be used as a reinterpretation tool. One important point which becomes clear once we compare figures 73 and 74 is the importance of a sufficiently inclusive database of simplified model efficiencies. In particular, depending on the full BSM scenario considered, the minimal set of simplified models proposed in chapter 2 and the appendix may not be sufficient to allow for a reinterpretation based on simplified model results alone. The reason is that this set was derived as the minimal set to generate a collection of relatively inclusive signatures, but may not correctly model the efficiency of every UV theory leading to that signature. In these cases, results for additional simplified model topologies are necessary and can be provided by the experimental collaborations or generated by theory groups if a full recasting is available. Furthermore, since LLP searches can be very inclusive, the simplified models considered can also be defined inclusively, as discussed above. In this way a limited number of simplified models can cover a large number of event topologies, thus increasing the SMS coverage of full models.

Searches for HSCPs are based on the signature of highly ionizing tracks and/or an anomalous TOF between the particle's production at the IP and its arrival in the muon detector [390] (see section 3.5.1.1 for more details). Both signatures are sensitive to the particle's velocity and exploit the production of HSCPs outside of the ultra-relativistic regime, allowing for a powerful discrimination against the highly boosted SM backgrounds. HSCP searches assume particles are sufficiently long-lived to traverse the entire detector. They have been interpreted for HSCPs that are purely electrically charged or carry color charge, the latter of which hadronize to form R-hadrons as they propagate through the detector [10]. Typically, the HSCP signature yields high sensitivities providing a very strong background rejection while still allowing for large signal efficiencies. As a consequence, search strategies for new physics models with HSCPs typically do not benefit from more model-dependent selection criteria, like requiring additional particles in the event [95]. The corresponding searches can, hence, be performed in a mostly inclusive manner concentrating on the HSCP candidate itself. This fact opens up the possibility of providing a widely applicable recasting based on signature efficiencies. This approach has been followed by the CMS Collaboration [495], which has provided probabilities for HSCP candidates to pass the on- and off-line selection criteria for Run 1 as a function of the relevant kinematical parameters.

In this section we describe the recasting of the 8 TeV CMS search for HSCPs and discuss its validation and applicability. Furthermore, we comment on the attempt to extrapolate the 8 TeV signature efficiencies to the corresponding 13 TeV analysis, for which the corresponding efficiencies have not been provided by CMS.

6.4.1.1. Recasting using signature efficiencies

Reference [495] provides efficiencies for the reconstruction and selection of HSCP candidates with $| Q| =1$ in the form of on- and off-line probabilities, ${P}_{\mathrm{on}}({\boldsymbol{k}})$ and ${P}_{\mathrm{off}}({\boldsymbol{k}})$. These are given as a function of the truth-level kinematic variables velocity (β), pseudo-rapidity (η) and transverse momentum (${p}_{{\rm{T}}}$) of isolated HSCP candidates, so the vector ${\boldsymbol{k}}$ is defined as: ${\boldsymbol{k}}=(\beta ,\eta ,{p}_{{\rm{T}}})$. The on- and off-line probabilities must be applied to isolated HSCP candidates, which are required to fulfill

$$\begin{eqnarray}&&\left(\displaystyle \sum _{i}^{\mathop{{\rm{\Delta }}R\lt 0.3}\limits^{\mathrm{charged}}}{p}_{{\rm{T}}}^{i}\right)\lt 50\,\mathrm{GeV},\quad \left(\displaystyle \sum _{i}^{\mathop{{\rm{\Delta }}R\lt 0.3}\limits^{\mathrm{visible}}}\displaystyle \frac{{E}^{i}}{| {\boldsymbol{p}}| }\right)\lt 0.3,\end{eqnarray} \tag{ 6.2 }$$

where the sums include all charged and visible particles, respectively, within a radius of ${\rm{\Delta }}R=\sqrt{{\rm{\Delta }}{\eta }^{2}+{\rm{\Delta }}{\phi }^{2}}\lt 0.3$ around the HSCP candidate track, ${p}_{{\rm{T}}}^{i}$ denotes their transverse momenta and Eⁱ their energy. Muons are not counted as visible particles and the HSCP itself is not included in either sum.

If an event contains one or more HSCPs satisfying the above isolation criteria, the efficiency for the event to pass the analysis selection is given by:

$$\begin{eqnarray}&&\epsilon ={\epsilon }_{\mathrm{on}}\times {\epsilon }_{\mathrm{off}}.\end{eqnarray} \tag{ 6.3 }$$

For an event with one HSCP candidate ${\epsilon }_{\mathrm{on}/\mathrm{off}}$ is directly given by the signature efficiencies ${P}_{\mathrm{on}/\mathrm{off}}({\boldsymbol{k}})$. For an event with two candidates, the efficiency reads [495]

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{on}/\mathrm{off}}={P}_{\mathrm{on}/\mathrm{off}}({{\boldsymbol{k}}}^{1})+{P}_{\mathrm{on}/\mathrm{off}}({{\boldsymbol{k}}}^{2})-{P}_{\mathrm{on}/\mathrm{off}}({{\boldsymbol{k}}}^{1}){P}_{\mathrm{on}/\mathrm{off}}({{\boldsymbol{k}}}^{2}),\end{eqnarray} \tag{ 6.4 }$$

where ${{\boldsymbol{k}}}^{\mathrm{1,2}}$ are the kinematical vectors of the two HSCPs in the given event. Therefore the on- and off-line probabilities combined with the isolation criteria allow for the complete recasting of the HSCP search using only truth-level events generated in MC.

The recasting of the 8 TeV search was performed in [97] using the procedure described above. Events were simulated using Pythia 6 [501] and the total signal efficiency for a given model was then computed using:

$$\begin{eqnarray*}&&\epsilon =\displaystyle \frac{1}{N}\displaystyle \sum _{i=1}^{N}{\epsilon }_{i},\end{eqnarray*}$$

where the sum runs over all the (N) generated events and _i is the efficiency for each event computed using equation (6.3). Since the probabilities ${P}_{\mathrm{on}/\mathrm{off}}({\boldsymbol{k}})$ are given for four distinct cuts on the reconstructed HSCP mass (m_rec), these were considered as four different signal regions. The number of observed events and the expected background for which of these cuts are reported in [495].

6.4.1.2. Validation and applicability

A validation of the method described above was done in [97] using the same GMSB model considered by CMS [495]. This supersymmetric model features a gravitino and a long-lived stau as the lightest and NLSP, respectively. Since the stau only decays outside the detector volume, all cascade decays of the produced sparticles terminate in the lightest stau, which provides the HSCP signature. The left pane of figure 75 compares the resulting signal efficiency obtained by the recasting and the full CMS detector simulation. The signal efficiencies agree within 3%, demonstrating that the recast is an excellent approximation to the full CMS simulation. The differences are of the order of the statistical uncertainties from the MC simulation of the signal. In the right pane of figure 75, we show the 95% C.L. upper limits on the inclusive production cross sections, which, again, agree (within ∼3%) with the ones obtained by the full simulation in [495]. Note that both limits are based on the discrete mass cuts on m_rec mentioned above. In the full CMS analysis [306], an event-based mass cut is used, resulting in slightly stronger constraints for some HSCP masses.

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Due to the inclusive nature of the search, the above recasting provides a widely applicable and highly reliable way to reinterpret the HSCP search for arbitrary models containing detector-stable HSCPs. Accordingly it has been used in a variety of phenomenological studies. For instance, it has been used for reinterpretations of supersymmetric models [96, 205, 502, 503] and non-supersymmetric models of very weakly interacting DM [142, 148]. In [96, 142], the recasting has been used to reinterpret the HSCP search for finite lifetimes by convolving the signature efficiency with the fraction of HSCPs that decay after traversing the relevant parts of the detector. The recasting has also been used for a reinterpretation in terms of simplified models, as discussed in section 6.3.2.

6.4.1.3. Extrapolation to 13 TeV

While the CMS search for HSCPs at 8 TeV has provided the signature efficiencies discussed above, the same is not true for the 13 TeV analysis [4]. Therefore a straightforward recasting of the Run 2 search is not possible. Nonetheless, since the 8 TeV CMS search has proven to be extremely useful in constraining models with long-lived charged particles, it would be desirable to recast the 13 TeV analysis as well. In the following we discuss an attempt [504] to obtain a similar recasting for the corresponding HSCP search at 13 TeV. Our aim is to extrapolate the public 8 TeV efficiencies to Run 2 by introducing a correction function F that accounts for the differences between both runs:

$$\begin{eqnarray}&&{P}_{\mathrm{off}}^{13\,\mathrm{TeV}}({\boldsymbol{k}})=F(\beta )\times {P}_{\mathrm{off}}^{8\,\mathrm{TeV}}({\boldsymbol{k}}),\end{eqnarray} \tag{ 6.5 }$$

where we have assumed that the correction function is mainly dependent on the HSCP velocity. If F(β) is sufficient to account for the difference between both runs and can be computed, we can directly obtain ${P}_{\mathrm{off}}^{13\,\mathrm{TeV}}$ and, using the procedure described in section 6.4.1.1, recast the 13 TeV analysis.

In order to compute the correction function F(β), we use the total signal efficiencies reported by the 13 TeV CMS analysis [4] for direct production of long-lived staus. Since the signal efficiencies have been provided for six distinct values of the stau mass, we perform a fit of F to the efficiencies reported. We chose to parametrize the correction function F(β) by eight parameters (C_i). Using MadGraph5_aMC@NLO [226] and Pythia 6 [501], we obtain generator-level events for each of the stau mass points at 13 TeV. Then, comparing the total signal efficiencies obtained for a given set C_i to the efficiencies reported in [4], we can determine the best-fit values for the C_i parameters and consequently the best-fit for the correction function (${F}_{\mathrm{best} \mbox{-} \mathrm{fit}}$). The result of the best-fit function and its 1σ uncertainty is shown in figure 76. The deviation of F from 1 implies a decrease or increase of the respective detector and signal efficiency between the 8 and 13 TeV analyses. Figure 76 also shows that the function is loosely constrained for low values of β.

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In order to verify the validity of the extrapolation to 13 TeV, we use ${F}_{\mathrm{best} \mbox{-} \mathrm{fit}}$ and equation (6.5) to compute the total signal efficiencies for the same six benchmark points used in the fit. A comparison between the results obtained through recasting and the efficiencies reported by CMS is shown by the second and third columns in table 6. The results reproduce the CMS values well within the expected uncertainties, thus validating the fitting procedure. Furthermore, the inclusion of the correction function significantly improves the agreement with respect to the direct extrapolation of the 8 TeV efficiencies (F = 1), as shown by the fourth column in table 6.

Table 6.  Efficiencies for the 13 TeV LHC for the six benchmark masses in the direct stau production scenario reported by CMS (second column) and obtained through recasting using ${F}_{\mathrm{best} \mbox{-} \mathrm{fit}}$ and without the inclusion of the correction function (F = 1).

	Direct production
mHSCP (GeV)	(CMS)	$\epsilon ({F}_{\mathrm{best} \mbox{-} \mathrm{fit}})$	(F = 1)
200	0.235	0.232	0.259
308	0.294	0.298	0.346
494	0.387	0.384	0.452
651	0.450	0.448	0.503
1029	0.497	0.501	0.466
1599	0.428	0.429	0.225

The high level of agreement obtained with ${F}_{\mathrm{best} \mbox{-} \mathrm{fit}}$ for the direct stau benchmark points is expected, since these points were used in order to fit the correction function. Therefore an independent test of the above fit must be performed in order to properly validate the recasting of the 13 TeV analysis. Fortunately CMS has also reported efficiencies for a second scenario, the GMSB model with long lived staus. This scenario not only contains direct stau production, but also includes production through cascade decays of heavier sparticles. Since the GMSB model produces distinct event topologies, it provides a good test for the validity of the recasting procedure.

The results for the six GMSB bechmark points considered in [4] are shown in table 7. As we can see, they deviate from the CMS values by up to 20% for large stau masses, where our estimate undershoots the CMS efficiencies. Although the overall agreement is improved by the correction function, the result is not entirely satisfactory, given that the uncertainties for the 8 TeV recasting were under 5% (see figure 75). The observed difference might arise from several shortcomings in our description.

Table 7.  Efficiencies for the 13 TeV LHC for the six GMSB model benchmark points reported by CMS (second column) and obtained through recasting using ${F}_{\mathrm{best} \mbox{-} \mathrm{fit}}$ and without the inclusion of the correction function (F = 1).

	GMSB
mHSCP (GeV)	(CMS)	$\epsilon ({F}_{\mathrm{best} \mbox{-} \mathrm{fit}})$	(F = 1)
200	0.276	0.297	0.279
308	0.429	0.401	0.423
494	0.569	0.494	0.556
651	0.628	0.524	0.580
1029	0.665	0.538	0.493
1599	0.481	0.442	0.228

In particular, we assume F to only depend on β whereas the full probability maps are parametrized in the three kinematic variables β, η and ${p}_{{\rm{T}}}$. However, assuming a dependence of all three kinematic variables is clearly not feasible given the very limited amount of information provided by the 13 TeV CMS analysis. Therefore we conclude that it is not possible to extrapolate the 8 TeV efficiencies in a straightforward way without additional information from the experimental collaboration.

Lessons learned. The prominent signature of HSCPs allows for a mostly inclusive search strategy concentrating on the HSCP track itself. Hence, searches for HSCPs can be reinterpreted using signature efficiencies in a widely applicable and highly reliable way. This possibility has been followed by the CMS Collaboration providing signature efficiency maps for the 8 TeV LHC. The validation reveals an excellent performance. The recast has been successfully used in the literature.

The signature efficiencies for 8 TeV can also be used to estimate the ones for Run 2 by applying a multiplicative correction function. While such an extrapolation introduces some level of approximation, a better knowledge of the underlying changes between both runs might reduce the uncertainties.