Ab initio structure factors for spin-dependent dark matter direct detection

Abstract

We present converged ab initio calculations of structure factors for elastic spin-dependent WIMP scattering off all nuclei used in dark matter direct-detection searches: $^{19}$F, $^{23}$Na, $^{27}$Al, $^{29}$Si, $^{73}$Ge, $^{127}$I, and $^{129,131}$Xe. From a set of established two- and three-nucleon interactions derived within chiral effective field theory, we construct consistent WIMP-nucleon currents at the one-body level, including effects from axial-vector two-body currents. We then apply the in-medium similarity renormalization group to construct effective valence-space Hamiltonians and consistently transformed operators of nuclear responses. Combining the recent advances of natural orbitals with three-nucleon forces expressed in large spaces, we obtain basis-space converged structure factors even in heavy nuclei. Generally results are consistent with previous calculations, but large uncertainties in $^{127}$I highlight the need for further study.