A complete Lorentz-to-Galileo dictionary for direct Dark Matter detection

Understand

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.