Impact of shell model interactions on WIMP-nucleus scattering observables for silicon and germanium targets

TL;DR

The paper investigates how nuclear-structure uncertainties arising from shell-model interactions affect WIMP-nucleus scattering observables for silicon and germanium targets in a SuperCDMS-like setup. It employs a non-relativistic EFT framework with SI, SD, LD, and LSD nuclear responses, computing $F^{(N,N')}_{X}(q^2)$ using large-scale shell-model calculations in the $sd$ (Si) and $f_{5}pg_9$ (Ge) spaces with USD/USDB and JUN45/jj44b interactions, respectively, and compares them to prior form-factor results via an Integrated Form Factor. Rates and exclusion curves are then propagated through detailed detector response models, yields, backgrounds, and a 5-year pseudo-data analysis using the Optimal Interval method under SHM. The results show that nuclear uncertainties at the form-factor level are largely retained in observable rates and limits, with Ge being particularly sensitive to LSD/SD channels and Si to SD channels, underscoring the importance of precise nuclear modelling for robust DM interpretation.

Abstract

The nature of dark matter (DM) remains one of the biggest mysteries in physics today. Dark matter direct detection experiments look for nuclear recoil signals from DM-nucleus elastic scattering, which can be used to characterise DM. Nuclear modelling of the target nucleus may impact the predicted DM-nucleus scattering rates, and affect interpretation of experimental signals. In this work, we investigate the impact of nuclear shell model interactions on DM nuclear responses for silicon and germanium targets using a SuperCDMS-like experimental parameters. Nuclear uncertainties resulting from shell model interaction choice in the nuclear form factors are roughly retained at the scattering rate and exclusion limit levels for certain nuclear responses.

Figures (4)

• Figure 1: Germanium interaction rates for the NR operators $\mathcal{O}_3^{\rm NR}$ and $\mathcal{O}_{12}^{\rm NR}$, for the shell model calculations GCN2850 (solid), JUN45 (dashed) and jj44b (dotted). Plotted using $m_\chi=10$ GeV/$c^2$ and $\sigma_p=10^{-40}$ cm$^2$.
• Figure 2: SuperCDMS-like germanium $\mathcal{O}_3^{\rm NR}$ and $\mathcal{O}_{12}^{\rm NR}$ projections curves for three shell model calculations.
• Figure 3: Silicon observation rates for the $\mathcal{O}_4^{\rm NR}$ and $\mathcal{O}_{10}^{\rm NR}$ operators, for the shell model calculations USD (solid) and USDB (dashed), using $m_\chi=10$ GeV/$c^2$ and $\sigma_p=10^{-40}$ cm$^2$.
• Figure 4: SuperCDMS-like silicon $\mathcal{O}_4^{\rm NR}$ and $\mathcal{O}_{10}^{\rm NR}$ projection curves for two shell model calculations.