Semiclassical regime for dark matter self-interactions

Physical review. D/Physical review. D., vol. 103

Abstract

Many particle physics models for dark matter self-interactions---motivated to address long-standing challenges to the collisionless cold dark matter paradigm---fall within the semiclassical regime, with interaction potentials that are long range compared to the de Broglie wavelength for dark matter particles. In this work, we present a quantum-mechanical derivation and new analytic formulas for the semiclassical momentum transfer and viscosity cross sections for self-interactions mediated by a Yukawa potential. Our results include the leading quantum corrections beyond the classical limit and allow for both distinguishable and identical dark matter particles. Our formulas supersede the well-known formulas for the momentum transfer cross section obtained from the classical scattering problem, which are often used in phenomenological studies of self-interacting dark matter. Together with previous approximation formulas for the cross section in the quantum regime, our new results allow for nearly complete analytic coverage of the parameter space for self-interactions with a Yukawa potential. We also discuss the phenomenological implications of our results and provide a new velocity-averaging procedure for constraining velocity-dependent self-interactions. Our results have been implemented in the newly released code CLASSICS.

Authors 5

1. Brian Colquhoun

   York University

   Affiliation as printed

   Department of Physics and Astronomy, York University,Toronto, Ontario M3J 1P3, Canada

2. Saniya Heeba Aachen Institute for Theoretical Particle Physics and Cosmology

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

3. Felix Kahlhoefer Aachen Institute for Theoretical Particle Physics and Cosmology

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

4. Laura Sagunski Aachen Institute for Theoretical Particle Physics and Cosmology

   Goethe University Frankfurt · RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

   Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, Germany

5. Sean Tulin

   York University

   Affiliation as printed

   Department of Physics and Astronomy, York University,Toronto, Ontario M3J 1P3, Canada