The Semi-Classical Regime for Dark Matter Self-Interactions
  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 semi-classical 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 semi-classical 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.
