It has been argued that the leading scalar-isoscalar weakly interacting massive particle (WIMP) -nucleus interactions receive parametrically enhanced contributions in the context of nuclear effective field theories [1]. These contributions arise from meson-exchange currents (MECs) and potentially modify the impulse approximation estimates of these interactions by 10%–60%. We point out that these MECs also contribute to the quark mass dependence of nuclear binding energies, that is, nuclear $\sigma$ terms. In this work, we use recent lattice QCD calculations of the binding energies of the deuteron, ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ at pion masses near 500 and 800 MeV, combined with the experimentally determined binding energies at the physical point, to provide approximate determinations of the $\sigma$ terms for these light nuclei. For each nucleus, we find that the deviation of the corresponding nuclear $\sigma$ term from the single-nucleon estimate is at the few-percent level, in conflict with the conjectured enhancement. As a consequence, lattice QCD calculations currently indicate that the cross sections for scalar-isoscalar WIMP-nucleus interactions arising from fundamental WIMP interactions with quarks do not suffer from significant uncertainties due to enhanced MECs.

• Received 15 August 2013

DOI:https://doi.org/10.1103/PhysRevD.89.074505