Dark matter scattering off <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">H</mml:mi><mml:mprescripts/><mml:none/><mml:mn>2</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http

We study dark matter, assumed to be composed of weak interacting massive particles (WIMPs), scattering off <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mrow/><a:mmultiscripts><a:mi mathvariant="normal">H</a:mi><a:mprescripts/><a:none/><a:mn>2</a:mn></a:mmultiscripts></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mrow/><c:mmultiscripts><c:mi>He</c:mi><c:mprescripts/><c:none/><c:mn>4</c:mn></c:mmultiscripts></c:mrow></c:math> nuclei. In order to parametrize the WIMP-nucleon interaction, the chiral effective field theory approach is used. Considering only interactions invariant under parity, charge conjugation, and time reversal, we examine five interaction types: scalar, pseudoscalar, vector, axial, and tensor. Scattering amplitudes between two nucleons and a WIMP are determined up to second order of chiral perturbation theory. We apply this program to calculate the interaction rate as a function of the WIMP mass and of the magnitude of the WIMP-quark coupling constants. From our study, we conclude that the scalar nuclear response functions is much greater than the others due to their large combination of low energy constants. We verify that the leading order contributions are dominant in these low energy processes. We also provide an estimate for the background due to atmospheric neutrinos. Published by the American Physical Society 2024