Large-scale nuclear structure calculations for spin-dependent WIMP scattering with chiral effective field theory currents

Abstract

We perform state-of-the-art large-scale shell-model calculations of the structure factors for elastic spin-dependent WIMP scattering off $^{129,131}\mathrm{Xe}$, $^{127}\mathrm{I}$, $^{73}\mathrm{Ge}$, $^{19}\mathrm{F}$, $^{23}\mathrm{Na}$, $^{27}\mathrm{Al}$, and $^{29}\mathrm{Si}$. This comprehensive survey covers the nonzero-spin nuclei relevant to direct dark matter detection. We include a pedagogical presentation of the formalism necessary to describe elastic and inelastic WIMP-nucleus scattering. The valence spaces and nuclear interactions employed have been previously used in nuclear structure calculations for these mass regions and yield a good spectroscopic description of these isotopes. We use spin-dependent WIMP-nucleus currents based on chiral effective field theory at the one-body level and including the leading long-range two-body currents due to pion exchange, which are predicted in chiral effective field theory. Results for all structure factors are provided with theoretical error bands due to the nuclear uncertainties of WIMP currents in nuclei.