The effective theory of nuclear scattering for a WIMP of arbitrary spin

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 $2j_{\chi }+1$ irreducible operator products of up to $2j_{\chi }$ 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.

47 pages, 4 figures, 8 tables

References in corpus (11)

• Nucleon Electromagnetic Form Factors
• Non-relativistic effective theory of dark matter direct detection
• Spin-Dependent Macroscopic Forces from New Particle Exchange
• From quarks to nucleons in dark matter direct detection
• Nuclear structure aspects of spin-independent WIMP scattering off xenon
• Global fits of the dark matter-nucleon effective interactions
• A Model Independent Approach to Inelastic Dark Matter Scattering
• Spin Dependence of Dark Matter Scattering
• Prospects for direct detection of dark matter in an effective theory approach
• Understanding WIMP-baryon interactions with direct detection: A Roadmap
• The phenomenology of nuclear scattering for a WIMP of arbitrary spin

Cited by in corpus (12)

• A Next-Generation Liquid Xenon Observatory for Dark Matter and Neutrino Physics
• WimPyDD: an object-oriented Python code for the calculation of WIMP direct detection signals
• Spin-dependent sub-GeV Inelastic Dark Matter-electron scattering and Migdal effect: (I). Velocity Independent Operator
• Dark Matter from Monogem
• The phenomenology of nuclear scattering for a WIMP of arbitrary spin
• Confronting spin-3/2 and other new fermions with the muon g-2 measurement
• Higher-spin particles at high-energy colliders
• Conservative constraints on the effective theory of dark matter-nucleon interactions from IceCube: the impact of operator interference
• Constructing the covariant three-point vertices systematically
• WimPyDD: an object-oriented Python code for WIMP-nucleus scattering direct detection in virtually any scenario
• Weaving the covariant three-point vertices efficiently
• Prospects for Dark Matter signal discovery and model selection via timing information in a low-threshold experiment