Dark quarkonium formation in the early universe

TL;DR

This paper investigates how heavy stable particles can form bound states called quarkonia in the early universe, affecting their relic abundance and providing insights for dark matter models and cosmology.

Contribution

It estimates the quarkonium formation cross section using a simple model, clarifying the process and its implications for dark matter and relic abundance calculations.

Findings

Quarkonium formation cross section is geometrically sized for rearrangement processes.

Mass-suppressed cross sections occur when only heavy constituents are involved.

Results apply to models with large bound states, impacting ultra-heavy dark matter theories.

Abstract

The relic abundance of heavy stable particles charged under a confining gauge group can be depleted by a second stage of annihilations near the deconfinement temperature. This proceeds via the formation of quarkonia-like states, in which the heavy pair subsequently annihilates. The size of the quarkonium formation cross section was the subject of some debate. We estimate this cross section in a simple toy model. The dominant process can be viewed as a rearrangement of the heavy and light quarks, leading to a geometric cross section of hadronic size. In contrast, processes in which only the heavy constituents are involved lead to mass-suppressed cross sections. These results apply to any scenario with bound states of sizes much larger than their inverse mass, such as U(1) models with charged particles of different masses, and can be used to construct ultra-heavy dark-matter models with masses above the na\"ive unitarity bound. They are also relevant for the cosmology of any stable colored relic.