Abstract
We determine the most general non-relativistic theory of DM-nucleon scattering complying with the sole requirement of Lorentz invariance, for spin-0 and spin-1/2 DM. To do so, we first classify a comprehensive list of amplitude terms encompassing the most general Lorentz-covariant 2-to-2 DM-nucleon scattering amplitude. We then match each term to a Galilean-invariant operator at leading-order in the non-relativistic expansion, for both elastic and inelastic (endothermic and exothermic) scattering. Our complete Lorentz-to-Galileo mapping can be used to promptly determine the non-relativistic DM-nucleon interaction and the associated nuclear form factor for any given Lorentz-invariant DM model. It applies to both renormalizable and non-renormalizable theories (such as effective field theories at all orders), at any order of a perturbative expansion. We use our results to prove that, at leading order, Lorentz invariance does not impose restrictions on the set of 16 Galilean-invariant operators commonly used to parametrize the non-relativistic DM-nucleon interaction. We also predict the lowest effective-operator dimension at which the non-relativistic operators appear in the effective field theory of a singlet DM particle.
Highlights
Direct dark matter (DM) search experiments aim at detecting the nuclear recoil of detector nuclei upon scattering with a DM particle
We provide here the leading-order NR theory of spin-0 and spin-1=2 DM particles interacting with nucleons through scalar, vector and tensor mediators, together with that of DM particles interacting with photons via a electric charge, a magnetic or electric dipole moment, and an anapole moment
NR Milky Way halo DM particles interact with whole nuclei within direct DM detection experiments
Summary
Direct dark matter (DM) search experiments aim at detecting the nuclear recoil of detector nuclei upon scattering with a DM particle. A possible reason could be that Lorentz invariance imposes stronger constraints on the scattering amplitude than the Galilean symmetry of the NR framework Some of these questions remain in the second approach, where the NR operators are studied regardless of their possible origin in a relativistic model. We provide a complete dictionary between the possible terms arising in a general 2-to-2 DM-nucleon scattering amplitude and the NR operators, assuming exclusively Lorentz invariance of the relativistic interaction. This approach, called heavy-particle effective theory, allows in a sense to integrate out the DM particle mass, which is large compared to the typical momentum transfer of a DM-nucleus scattering process, without completely integrating out the DM field [26,27,28,29,30,31] This expansion method was applied to the effective field theory of a spin-1=2 DM particle, singlet under the Standard Model (SM) gauge group, in Ref.
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