Dark Matter Sommerfeld-enhanced annihilation and Bound-state decay at finite temperature

TL;DR

This paper develops a first-principles quantum field theory approach to accurately model dark matter interactions, including bound states and thermal effects, leading to a new differential equation for DM abundance that generalizes traditional models.

Contribution

It introduces a comprehensive ab-initio derivation of dark matter interactions in a hot plasma, accounting for mixing of scattering and bound states at finite temperature.

Findings

Derived a novel temperature-independent differential equation for DM number density.

Unified the description of annihilation and bound state decay in a non-quadratic collision term.

Demonstrated consistency with previous models in certain limits.

Abstract

Traditional computations of the dark matter (DM) relic abundance, for models where attractive self-interactions are mediated by light force-carriers and bound states exist, rely on the solution of a coupled system of classical on-shell Boltzmann equations. This idealized description misses important thermal effects caused by the tight coupling among force-carriers and other charged relativistic species. We develop for the first time a comprehensive ab-initio derivation for the description of DM long-range interactions in the presence of a hot and dense plasma background directly from non-equilibrium quantum field theory. Most importantly, the scattering and bound states get strongly mixed in the thermal plasma environment, representing a characteristic difference from a pure vacuum theory computation. The main result of this work is a novel differential equation for the DM number density, written down in a form which is manifestly independent under the choice of what one would interpret as a bound or a scattering state at finite temperature. The collision term, unifying the description of annihilation and bound state decay, turns out to have in general a non-quadratic dependence on the DM number density. This generalizes the form of the conventional Lee-Weinberg equation which is typically adopted to describe the freeze-out process. We prove that our general number density equation is consistent with previous literature results under certain limits.