Unitarity in the non-relativistic regime and implications for dark matter

TL;DR

This paper explores how unitarity constraints in the non-relativistic regime, especially due to long-range interactions, can be restored through resummation techniques, impacting dark matter physics.

Contribution

It introduces a model-independent resummation method to unitarize cross-sections affected by long-range interactions in the non-relativistic regime.

Findings

Resummation unitarizes elastic and inelastic cross-sections.

Method applies to all partial waves and is model-independent.

Implications for dark matter phenomenology.

Abstract

Unitarity sets upper limits on partial-wave elastic and inelastic cross-sections, which are often violated by perturbative computations. We discuss the dynamics underlying these limits in the non-relativistic regime, namely long-range interactions, and show how the resummation of the 2-particle-irreducible diagrams arising from squaring inelastic processes unitarizes both elastic and inelastic cross-sections. We provide a simple prescription to obtain the unitarized cross-sections from those that do not include resummation of the squared inelastic processes. Our results are model-independent, apply to all partial waves, and affect elastic and inelastic cross-sections, with extensive implications for new physics scenarios, such as dark-matter freeze-out, indirect detection and self-interactions.