Nuclear σ terms and scalar-isoscalar WIMP-nucleus interactions from lattice QCD

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, He-3 and He-4 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.