Unitarity violation and restoration in radiative bound-state formation

TL;DR

This paper investigates unitarity violations in radiative bound-state formation calculations relevant to dark matter physics and demonstrates how proper resummation of inelastic contributions restores unitarity, with implications for phenomenology.

Contribution

It derives new formulas for partial waves and shows how to restore unitarity through resummation of absorptive self-energy contributions in bound-state formation.

Findings

Existing calculations violate unitarity in partial waves.

Resummation of inelastic contributions restores unitarity.

Results applicable to dark matter phenomenology.

Abstract

State-of-the-art calculations motivated by dark matter exhibit severe violation of partial-wave unitarity in the non-relativistic regime in radiative bound-state-formation processes. It has been recently shown, in a model-independent fashion, that unitarity is restored by the proper resummation of the inelastic contributions to the self-energy of the incoming state. In this work, we first derive Kramers-like formulae for individual partial waves, demonstrating that existing calculations of bound-state formation severely violate unitarity. We then discuss how unitarity is restored through the resummation of the absorptive contributions to the incoming-state self-energy, generated by bound-state formation processes, taking into account their analytic structure in the complex momentum plane. Our results can be generalized in a variety of theories and employed in phenomenological studies, such as dark-matter freeze-out, indirect detection and self-interactions.