Bound-state formation for thermal relic dark matter and unitarity

TL;DR

This paper investigates how bound-state formation influences the relic abundance of thermal dark matter with long-range interactions, establishing upper mass bounds and emphasizing the importance of bound states in early universe annihilations.

Contribution

It provides an analytical framework for calculating dark matter relic abundance including bound states and derives upper mass limits based on unitarity constraints.

Findings

Bound-state formation significantly impacts relic abundance calculations.

Upper mass limit for thermal dark matter is approximately 197 TeV for self-conjugate cases.

Unitarity limit is achieved only with long-range interactions.

Abstract

We show that the relic abundance of thermal dark matter annihilating via a long-range interaction, is significantly affected by the formation and decay of dark matter bound states in the early universe, if the dark matter mass is above a few TeV. We determine the coupling required to obtain the observed dark matter density, taking into account both the direct 2-to-2 annihilations and the formation of bound states, and provide an analytical fit. We argue that the unitarity limit on the inelastic cross-section is realized only if dark matter annihilates via a long-range interaction, and we determine the upper bound on the mass of thermal-relic dark matter to be about 197 (139) TeV for (non)-self-conjugate dark matter.