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Complete Lorentz-to-Galileo dictionary for direct dark matter detection

Eugenio Del Nobile*

  • School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *eugenio.delnobile@nottingham.ac.uk
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Phys. Rev. D 98, 123003 – Published 10 December, 2018

DOI: https://doi.org/10.1103/PhysRevD.98.123003

Abstract

We determine the most general nonrelativistic theory of dark matter (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 nonrelativistic expansion, for both elastic and inelastic (endothermic and exothermic) scattering. Our complete Lorentz-to-Galileo mapping can be used to promptly determine the nonrelativistic DM-nucleon interaction and the associated nuclear form factor for any given Lorentz-invariant DM model. It applies to both renormalizable and nonrenormalizable 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 nonrelativistic DM-nucleon interaction. We also predict the lowest effective-operator dimension at which the nonrelativistic operators appear in the effective field theory of a singlet DM particle.

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Phys. Rev. D 98, 123003– Published 10 December, 2018
  • Received 21 September 2018
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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