Quantum Monte Carlo calculations of dark matter scattering off light nuclei

We compute the matrix elements for elastic scattering of dark matter (DM) particles off light nuclei (${}^2\mathrm{H}, {}^3\mathrm{H}, {}^3\mathrm{He}, {}^4\mathrm{He}$, and ${}^6\mathrm{Li}$) using quantum Monte Carlo methods. We focus on scalar-mediated DM-nucleus interactions and use scalar currents obtained to next-to-leading order in chiral effective theory. The nuclear ground states are obtained from a phenomenological nuclear Hamiltonian that includes the Argonne $v_{18}$ two-body interaction and the three-body Urbana IX interaction. Within this approach, we study the impact of one- and two-body currents and discuss the size of nuclear uncertainties, including for the first time two-body effects in $A=4$ and $A=6$ systems. Our results provide the nuclear structure input needed to assess the sensitivity of future experimental searches of (light) dark matter using light nuclei, such as ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$.

Figure 1

Diagrams contributing to DM-nucleus scattering up to NLO. Solid black lines denote nucleons; dashed lines denote pions. (a) Interaction at leading order (LO). (b) One-body interaction at NLO. (c) Two-body interaction at NLO.

Figure 2

Isoscalar matrix elements for nuclei from $A=2$ to 6. Dashed blue lines correspond to LO calculations, and orange solid ones correspond to NLO.

Figure 3

Percentual radius correction for ${}^4\mathrm{He}$.

Figure 4

Percentual two-body correction to the total cross section for various nuclei.

Figure 5

Percentual two-body correction to the total cross section for various nuclei.

Figure 6

Cutoff dependence of the two-body contribution for $q=0$.