Effective field theory analysis of the first LUX dark matter search

D. S. Akerib et al. (LUX Collaboration)

Phys. Rev. D 103, 122005 – Published 22 June 2021

Abstract

The Large Underground Xenon (LUX) dark matter search was a 250-kg active mass dual-phase time projection chamber that operated by detecting light and ionization signals from particles incident on a xenon target. In December 2015, LUX reported a minimum 90% upper C.L. of $6 \times 10^{- 46} {cm}^{2}$ on the spin-independent WIMP-nucleon elastic scattering cross section based on a $1.4 \times 10^{4} kg \cdot day$ exposure in its first science run. Tension between experiments and the absence of a definitive positive detection suggest it would be prudent to search for WIMPs outside the standard spin-independent/spin-dependent paradigm. Recent theoretical work has identified a complete basis of 14 independent effective field theory (EFT) operators to describe WIMP-nucleon interactions. In addition to spin-independent and spin-dependent nuclear responses, these operators can produce novel responses such as angular-momentum-dependent and spin-orbit couplings. Here we report on a search for all 14 of these EFT couplings with data from LUX’s first science run. Limits are placed on each coupling as a function of WIMP mass.

Received 26 March 2020
Revised 5 May 2021
Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevD.103.122005

Physics Subject Headings (PhySH)

Particle astrophysics Particle dark matter

Dark matter detectors

Gravitation, Cosmology & Astrophysics

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Vol. 103, Iss. 12 — 15 June 2021

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Images

Figure 1
The relative size of integrated nuclear form factors $\int_{0}^{100 MeV} \frac{1}{2} q F_{k} (q^{2}) d q$ by target for $k = M, Σ^{''}, Σ^{'}, Δ, Φ^{''}$ , and ${\tilde{Φ}}^{'}$ , adapted and expanded from Fig. 1 of [17]. The contribution of each isotope is weighted by natural abundance. Each value is normalized by that of the element with the maximum integrated form factor.
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Figure 2
WIMP-nucleon recoil spectra in xenon for a representative sample of EFT operators, weighted by the natural abundance of isotopes. We assume a spin- $1 / 2$ WIMP that obeys a Maxwellian WIMP velocity distribution with a characteristic velocity $v_{0} = 220 km / s$ and escape velocity $v_{esc} = 544 km / s$ . The spectra are normalized so that the coupling constant $c_{1}^{(n, p)}$ produces a zero-momentum transfer WIMP-nucleon interaction cross section of $1 \times 10^{- 36} {cm}^{2}$ for operator $O_{1}$ . For the other operators $O_{i}$ , we set $c_{i} = c_{1}$ . For comparison, we also show the recoil spectra for the standard SI WIMP-nucleon interactions assuming a Helm form factor [28] and recoil spectra for the standard SD WIMP-nucleon interactions using the structure factors calculated in [29].
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Figure 3
LUX detector efficiencies used to define the search window for WIMPs undergoing EFT interactions with xenon nuclei in the LUX target. The extension of the search window to higher energies is important as many EFT operators have significant signal response at energies much higher than in the standard WIMP search. The background-discrimination cut ( $\sim 50 %$ acceptance) is not included in this plot.
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Figure 4
All events in the 95-liveday LUX 2013 WIMP search dataset in $\log_{10} (S 2)$ vs S1 parameter space, for a 118-kg fiducial volume, after all cuts. The solid blue curve indicates the median of the NR band as predicted by NEST, which has been tuned to NR calibration data (this differs slightly from LUX standard WIMP analysis of the same data, which used the NR band as measured with calibration data). The dashed blue line shows the corresponding median— $3 σ$ contour. Events that lie between the solid and dashed blue lines are highlighted as red squares. The gray curve is a contour of constant energy (corresponding to NRs of 150 keV), and defines the upper boundary of the search window; it is chosen to remove events originating from the decay of ${}^{83 m}{Kr}$ (dense population of black points). Overall, nine events appear in the signal region.
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Figure 5
Simulated ER background event density in LUX for a 118-kg fiducial volume (18-cm radius). The median (solid blue) and median— $3 σ$ (dashed blue) contours of the NR band are shown. The WIMP signal region is defined as the region between these two blue contours, up to the gray contour which represents a nuclear recoil energy ( $E_{NR}$ ) of 150 keV.
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Figure 6
Limits on the WIMP-neutron and WIMP-proton coupling constants associated with an example selection of EFT operators $O_{1}$ (the standard SI operator, no dependence on momentum $q$ ), $O_{3}$ (generates $Σ^{'}$ and $Φ^{''}$ responses proportional to $q^{2}$ ), $O_{4}$ (a spin-dependent operator with no dependence on $q$ ), $O_{5}$ (generates M and $Δ$ responses proportional to $q^{2}$ ), $O_{6}$ (generates a $Σ^{''}$ response proportional to $q^{4}$ ), $O_{9}$ (generates a $Σ^{'}$ response proportional to $q^{2}$ ), $O_{11}$ (generates an M response proportional to $q^{2}$ ), and $O_{13}$ (generates $Σ^{''}$ and ${\tilde{Φ}}^{'}$ responses proportional to $q^{2}$ ).
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