ReviewDiquark correlations in hadron physics: Origin, impact and evidence
Introduction
More than one century of fundamental research in atomic and nuclear physics has shown that all matter is corpuscular, with the atoms that comprise us, themselves containing a dense nuclear core. This core is composed of protons and neutrons, referred to collectively as nucleons, which are members of a broader class of fm-scale particles, called hadrons. In working towards an understanding of hadrons, it has been found that they are complicated bound states of gluons and quarks whose interactions are described by a Poincaré-invariant quantum non-Abelian gauge field theory; namely, quantum chromodynamics (QCD).
QCD is fundamentally different from other pieces of the Standard Model of Particle Physics (SM): whilst perturbation theory is a powerful tool when used in connection with high-energy processes, this technique is powerless when it comes to developing an understanding of observable low-energy characteristics of QCD. The body of experimental and theoretical methods used to probe and map QCD’s infrared domain can be called strong-QCD [1] and they must deal with emergent nonperturbative phenomena, such as confinement of gluons and quarks and dynamical chiral symmetry breaking (DCSB).
The QCD running coupling lies at the heart of many attempts to define and understand confinement because almost immediately following the demonstration of asymptotic freedom [2], [3], [4] the associated appearance of an infrared Landau pole in the perturbative expression for the running coupling spawned the idea of infrared slavery, viz. confinement expressed through a far-infrared divergence in the running coupling. In the absence of a nonperturbative definition of a unique running coupling, this idea is not more than a conjecture; but recent studies [5], [6], [7] support a conclusion that the Landau pole is screened (eliminated) in QCD by the dynamical generation of a gluon mass-scale and the theory possesses an infrared stable fixed point.
In numerical simulations of lattice-regularised QCD (lQCD) that use static sources to represent the valence-quarks of, for instance, a proton, a “Y-junction” flux-tube picture of nucleon structure is drawn, e.g. Refs. [8], [9]. Such results and notions could suggest an important role for the three-gluon vertex, which is a signature of the non-Abelian character of QCD and the source of asymptotic freedom, in quark (and gluon) confinement inside the hadron. That is, if the static-quark picture were equally valid in real-world QCD. In dynamical QCD, however, wherein active light quarks are ubiquitous, it is not; so a different explanation of binding within the nucleon, and most generally within any hadron, must be found.
Based on an accumulated body of evidence, it appears likely that confinement, defined via the violation of reflection positivity by coloured Schwinger functions (see, e.g. Refs. [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27] and citations therein and thereof) and DCSB have a common origin in the SM; but this does not mean that confinement and DCSB must necessarily appear together. Models can readily be built that express one without the other, e.g. numerous constituent quark models express confinement through potentials that rise rapidly with interparticle separation, yet possess no ready definition of a chiral limit [28], [29]; and models of the Nambu–Jona-Lasinio type typically express DCSB but not confinement [30], [31], [32].
DCSB ensures the existence of nearly-massless pseudo-Nambu–Goldstone (NG) modes (pions), each constituted from a valence- quark and-antiquark whose individual Lagrangian current-quark masses are % of the proton mass [33]. In the presence of these modes, no flux tube between a static colour source and sink can have a measurable existence. To verify this statement, consider such a tube being stretched between a source and sink. The potential energy accumulated within the tube may increase only until it reaches that required to produce a particle–antiparticle pair of the theory’s pseudo-NG modes. Simulations of lQCD show [34], [35] that the flux tube then disappears instantaneously along its entire length, leaving two isolated colour-singlet systems. The length-scale associated with this effect in QCD is . Hence, if any such string forms, it would dissolve well within hadron interiors.
Another equally important consequence of DCSB is less well known. Namely, any interaction capable of creating pseudo-NG modes as bound states of a light dressed- quark and-antiquark, and reproducing the measured value of their leptonic decay constants, will necessarily also generate strong colour–antitriplet correlations between any two dressed quarks contained within a hadron. Although a rigorous proof within QCD is not known, this assertion is based upon an accumulated body of evidence, gathered in three decades of studying two- and three-body bound-state problems in hadron physics, e.g. Refs. [36], [37], [38], [39], [40], [41], [42], [43], [44]. No realistic counter examples are known; and the existence of such quark+quark (diquark) correlations is also supported by simulations of lQCD [45], [46], [47], [48], [49], [50], [51].
It is worth remarking here that in a dynamical theory based on SU-colour, diquarks are colour singlets. They would thus exist as asymptotic states and form mass-degenerate multiplets with mesons composed from like-flavoured quarks. (These properties are a manifestation of Pauli–Gürsey symmetry [52], [53].) Consequently, the isoscalar–scalar, , diquark would be massless in the presence of DCSB, matching the pion, and the isovector–pseudovector, , diquark would be degenerate with the theory’s -meson. Such identities are lost in changing the gauge group to SU-colour [SU]; but clear and instructive similarities between mesons and diquarks nevertheless remain, such as [20], [36], [41], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65]: (i) isoscalar–scalar and isovector–pseudovector diquark correlations are the strongest, but others could appear inside a hadron so long as their quantum numbers are allowed by Fermi–Dirac statistics; (ii) the associated diquark mass-scales express the strength and range of the correlation and are each bounded below by the partnered meson’s mass; and (iii) realistic diquark correlations are soft, i.e. they possess an electromagnetic size that is bounded below by that of the analogous mesonic system.
It is important to appreciate that these fully dynamical diquark correlations are different from the static, pointlike diquarks which featured in early attempts [66] to understand the baryon spectrum and to explain the so-called missing resonance problem [67], [68], [69]. Modern diquarks are fully dynamical inside hadrons: no valence quark holds a special place because each one participates in all diquarks to the fullest extent allowed by the quantum numbers of the quark, the diquark and the hadron in hand. The continual rearrangement of the quarks guarantees a hadron spectrum as rich as that found experimentally and that obtained in modern constituent quark models [29] and lQCD calculations [70].
Evidently, the notion of diquark correlations is spread widely across modern nuclear and high-energy physics; for example, experiment has uncovered signals for such correlations in the flavour-separation of the proton’s electromagnetic form factors [71], [72]; and phenomenology suggests that diquark correlations might play a material role in the formation of exotic tetra- and penta-quark hadrons [73], [74], [75], [76], [77], [78], [79]. At issue, however, is whether all these things called diquarks are the same; and if there are dissimilarities, can they be understood and reconciled so that experiment can properly search for clean observable signals.
Herein, therefore, a critical review of existing information is undertaken in order to consolidate available facts and identify a path toward a consistent description of diquark correlations inside hadrons that answers the following basic questions:
- (i)
How firmly founded are continuum theoretical predictions of diquark correlations in hadrons?
- (ii)
What does lQCD have to say about the existence and character of diquark correlations in baryons and multiquark systems?
- (iii)
Are there strategies for combining continuum and lattice methods in pursuit of an insightful understanding of hadron structure?
- (iv)
Can theory identify experimental observables that would constitute unambiguous measurable signals for the presence of diquark correlations?
- (v)
Is there a traceable connection between the so-called diquarks used to build phenomenological models of high-energy processes and the correlations predicted by contemporary theory; and if so, how can such models be improved therefrom?
- (vi)
Are diquarks the only type of two-body correlations that play a role in hadron structure?
- (vii)
Which new experiments, facilities and analysis tools are best suited to test the emerging picture of two-body correlations in hadrons?
Note, too, that the last millennium saw publications which treat the diquark concept explicitly or implicitly. It is not our intention to recapitulate that work. Interested parties may consult other documents that supply additional material, e.g. Refs. [66], [80], the proceedings of some workshops in the 1990s [81], [82], [83], and a compilation of references to articles on diquarks [84].
Before proceeding further, it is worth remarking that this perspective supplies a wide-ranging view of the diquark concept, providing a discussion of many variations on the theme. There are some occasions in which different approaches might appear to be mutually inconsistent. In such cases, the reader should understand that in science there is room for constructive disagreement on the road of progress.
The manuscript is arranged as follows. In Section 2 we revisit the theoretical concept of diquark correlations inside hadrons; review the latest advances on this topic using phenomenological quark models, continuum Schwinger functional methods and lattice-regularised QCD techniques; and highlight some examples of their most relevant results compared with experimental data. Section 3 is devoted to an experimental overview of the most prominent signals of diquark correlations inside hadrons, either conventional or unconventional. We dedicate Section 4 to discuss possible theoretical and experimental pathways, which have not yet been explored and can consolidate the concept of diquark correlations. We finish with a summary and perspective in Section 5.
Section snippets
Phenomenological quark models
The notion of diquarks dates back to the foundations of the quark model (QM) itself [85], [86]. Its introduction had the purpose to provide an alternative description of baryons as bound states of a constituent-quark and -diquark [87], [88], [89]. Later, phenomenological indications for the emergence of diquark-like correlations were given. They included the rule in weak non-leptonic decays [90]; some regularities in parton distribution functions (DFs) and spin-dependent structure
Space-like nucleon form factors
Nucleon structure investigations using high energy electron scattering have been a successful field of discoveries since 1955, with the determination of the proton size [349]. The status of the current knowledge of nucleon electromagnetic form factors is reviewed in Refs. [350], [351]. To a large extent, this success owes to the dominance of the one-photon exchange mechanism in electron scattering as proposed in the original theory [352].
The most decisive studies of the partonic structure of
Super bigbite spectrometer programme on high- space-like nucleon form factors
The electromagnetic form factors (EMFFs) measured in elastic lepton–nucleon scattering are key elements in resolving the role of diquark correlations in nucleon structure. At large momentum transfers, the unpolarised differential scattering cross-section is dominated by the magnetic form factor, . On the other hand, the ratio of the electric and magnetic form factors at high- is best determined using polarisation observables. To measure the EMFFs at large values of is very challenging
Epilogue
Modern facilities will probe hadronic interiors as never before, e.g. JLab at 12 GeV will push form factor measurements to unprecedented values of momentum transfer and use different charge states, enabling flavour separations; an EIC and EicC would measure valence-quark distribution functions with previously unattainable precision; and elsewhere, collaborations like BaBar, Belle, BESIII, LHCb, are discovering new hadrons whose structure does not fit once viable paradigms. The wealth of new and
Abbreviations
The following abbreviations are used in this manuscript:
ACC aerogel threshold Cherenkov counters BABAR detector at SLAC Belle (Belle-II) detector at Japan’s high energy accelerator research complex in Tsukuba BEPC (BEPCII) Beijing Electron Positron Collider BESIII detector at BEPC BL19 Analysis framework in Refs. [612], [613] BoNuS detector and associated collaboration at JLab BS (BSE) Bethe–Salpeter (equation) CDC central drift chamber CEBAF Continuous Electron Beam Accelerator Facility at JLab CERN European
Acknowledgements
We are particularly grateful to Daniele Binosi and Susan Driessen for their hospitality, support and help during the ECT Workshop “Diquark Correlations in Hadron Physics: Origin, Impact and Evidence”, held in Trento, Italy, September 23–27, 2019, from which emerged the perspective contained herein. Work supported by: Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico, under the Estancias posdoctorales en el extranjero (EPE-2019) program; Agencia Nacional de Investigación y Desarrollo
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