Radiation back-reaction during dark-matter freeze-out via metastable bound states

Abstract

The formation and decay of metastable bound states can deplete significantly the density of multi-TeV thermal-relic dark matter. The effect depends on the interplay of bound-state formation, ionisation, transition and decay processes. Existing calculations take into account bound-state ionisation and excitations due to the radiation of the thermal bath. However, the dynamics of Hydrogen recombination suggests that the resonant radiation produced in bound-state formation or de-excitations may backreact, ionising or exciting the bound states thus impeding recombination. In this paper we examine this effect in the context of dark-matter freeze-out. To this end, we employ the generalised Saha equilibrium equation for metastable bound states, and discuss its salient features. We show that, in sharp contrast to Hydrogen recombination, the radiation produced during dark matter freeze-out is more likely to thermalise or redshift, rather than ionise or excite the metastable bound states.This holds not only for the low-energy (resonant) radiation produced in bound-state formation and transition processes, but also for the high-energy radiation produced in dark-matter annihilations and bound-state decays. While our computations are carried out in a minimal dark U(1) model, our conclusions only strengthen in more complex models.