On the classical description of the recombination of dark matter particles with a Coulomb-like interaction

TL;DR

This paper compares classical and quantum approaches to dark matter particle recombination with Coulomb-like interactions, showing classical methods predict a much lower residual unbound dark matter density after decoupling.

Contribution

It demonstrates that classical treatment of dark matter recombination significantly alters the predicted residual density compared to quantum calculations, impacting dark matter models with long-range interactions.

Findings

Classical cross sections depend steeply on relative velocity.

Recombination does not freeze out, reducing unbound dark matter density.

Residual density differs by about five orders of magnitude from quantum estimates.

Abstract

Cold dark matter (DM) scenario may be cured of several problems by involving self-interaction of dark matter. Viability of the models of long-range interacting DM crucially depends on the effectiveness of recombination of the DM particles, making thereby their interaction short-range. Usually in numeric calculations, recombination is described by cross section obtained on a feasible quantum level. However in a wide range of parameter values, a classical treatment, where the particles are bound due to dipole radiation, is applicable. The cross sections, obtained in both approaches, are very different and lead to diverse consequences. Classical cross section has a steeper dependence on relative velocity, what leads to the fact that, after decoupling of DM particles from thermal background of "dark photons" (carriers of DM long-range interaction), recombination process does not "freeze out", diminishing gradually density of unbound DM particles. Our simplified estimates show, that at the taken parameter values (the mass of DM particle is $100$ GeV, interaction constant is $100^{-1}$, and quite natural assumptions on initial conditions, from which the result is very weakly dependent) the difference in residual density reaches about $5$ orders of magnitude on pre-galactic stage. This estimate takes into account thermal effects induced by dipole radiation and recombination, which resulted in the increase of both temperature and density of DM particles by a half order of magnitude.