Effective theory of nuclear scattering for a WIMP of arbitrary spin

Paolo Gondolo,Gaurav Tomar,Sunghyun Kang,Stefano Scopel

doi:10.1103/physrevd.104.063017

Paolo Gondolo, Gaurav Tomar + Show 2 more

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https://doi.org/10.1103/physrevd.104.063017

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Abstract

We introduce a systematic approach to characterize the most general non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin $j_\chi$ in the approximation of one-nucleon currents. Five nucleon currents arise from the nonrelativistic limit of the free nucleon Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents according to the rank of the $2 j_\chi+1$ irreducible operator products of up to $2 j_\chi$ WIMP spin vectors, and (2) coupling each of the WIMP currents to each of the five nucleon currents. The transferred momentum $q$ appears to a power fixed by rotational invariance. For a WIMP of spin $j_\chi$ we find a basis of 4+20$j_\chi$ independent operators that exhaust all the possible operators that drive elastic WIMP-nucleus scattering in the approximation of one-nucleon currents. By comparing our operator basis, which is complete, to the operators already introduced in the literature we show that some of the latter for $j_\chi=1$ were not independent and some were missing. We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments.

Highlights

In one of its most popular scenarios dark matter (DM) is believed to be composed of weakly interacting massive particles (WIMPs) with a mass in the GeV-TeV range and weak-type interactions with ordinary matter
We introduce a systematic approach to characterize the most general nonrelativistic weakly interacting massive particle (WIMP)-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin jχ in the approximation of one-nucleon currents and for a WIMP-nucleon effective potential at most linear in the velocity
We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments

Summary

Introduction

In one of its most popular scenarios dark matter (DM) is believed to be composed of weakly interacting massive particles (WIMPs) with a mass in the GeV-TeV range and weak-type interactions with ordinary matter. Such small but nonvanishing interactions can drive WIMP scattering off nuclear targets, and the measurement of the ensuing nuclear recoils in low-background detectors (direct detection, DD) represents the most straightforward way to detect them. The most popular WIMP candidates are provided by extensions of the Standard Model such as supersymmetry or large extra dimensions, which are in growing tension with the constraints from the Large Hadron Collider.

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