Reanalysis of nuclear spin matrix elements for dark matter spin-dependent scattering

Abstract

We show how to include in the existing calculations for nuclei other than ${}^{129}$Xe, ${}^{131}$Xe, the corrections to the isovector coupling arising in chiral effective field theory recently found in Ref. \cite{Menendez1}. The dominant, momentum independent, 2-body currents effect can be taken into account by formally redefining the static spin matrix elements $<{\mathbf{S}}_{p,n}>$. By further using the normalized form factor at $q\ne 0$ built with the 1-body level structure functions, we show that the WIMP-nucleus cross section and the upper limits on the WIMP-nucleon cross sections coincide with the ones derived using the exact functions at the 2-body level. We explicitly show it in the case of XENON100 limits on the WIMP-neutron cross section and we recalculate the limits on the WIMP-proton spin dependent cross section set by COUPP. We also give practical formulas to obtain $<{\mathbf{S}}_{p,n}>$ given the structure functions in the various formalisms/notations existing in literature. We argue that the standard treatment of the spin-dependent cross section in terms of three independent isospin functions, $S_{00}(q)$, $S_{11}(q)$, $S_{01}(q)$, is redundant in the sense that the interference function $S_{01}(q)$ is the double product $|S_{01}(q)|=2\sqrt{S_{00}(q)}\sqrt{S_{11}(q)}$ even when including the new effective field theory corrections.

8 pages, 6 figures: extended and revised, accepted in Physical Review D

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• Lipkin model on a quantum computer
• Light Dark Matter Anomalies After LUX
• Vector Fermion-Portal Dark Matter: Direct Detection and Galactic Center Gamma-Ray Excess
• Direct detection and solar capture of spin-dependent dark matter
• Probing WIMP particle physics and astrophysics with direct detection and neutrino telescope data
• Reconstructing the three-dimensional local dark matter velocity distribution
• Discretising the velocity distribution for directional dark matter experiments
• A Spin-Dependent Interpretation for Possible Signals of Light Dark Matter
• Renormalization of the Spin-dependent WIMP scattering off nuclei