Effective field theories for dark matter pairs in the early universe: center-of-mass recoil effects

TL;DR

This paper develops effective field theories to accurately account for recoil effects in dark matter pair interactions within the early universe, impacting relic density calculations and applicable to other systems like quarkonia and atomic clocks.

Contribution

It introduces a field theory framework to include recoil effects in dark matter pair interactions, improving precision in relic density estimates and related phenomena.

Findings

Recoil effects significantly influence dark matter annihilation and bound-state formation rates.

Lorentz transformations of interaction quantities are explicitly verified.

Recoil corrections impact the estimated dark matter energy density in the early universe.

Abstract

For non-relativistic thermal dark matter, close-to-threshold effects largely dominate the evolution of the number density for most of the times after thermal freeze-out, and hence affect the cosmological relic density. A precise evaluation of the relevant interaction rates in a thermal medium representing the early universe includes accounting for the relative motion of the dark matter particles and the thermal medium. We consider a model of dark fermions interacting with a plasma of dark gauge bosons, which is equivalent to thermal QED. The temperature is taken to be smaller than the dark fermion mass and the inverse of the typical size of the dark fermion-antifermion bound states, which allows for the use of non-relativistic effective field theories. For the annihilation cross section, bound-state formation cross section, bound-state dissociation width and bound-state transition width of dark matter fermion-antifermion pairs, we compute the leading recoil effects in the reference frame of both the plasma and the center-of-mass of the fermion-antifermion pair. We explicitly verify the Lorentz transformations among these quantities. We evaluate the impact of the recoil corrections on the dark matter energy density. Our results can be directly applied to account for the relative motion of quarkonia in the quark-gluon plasma formed in heavy-ion collisions. They may be also used to precisely assess thermal effects in atomic clocks based on atomic transitions; the present work provides a first field theory derivation of time dilation for these processes in vacuum and in a medium.