Perturbative Unitarity of Strongly Interacting Massive Particle Models

TL;DR

This paper investigates the perturbative unitarity constraints in strongly interacting massive particle models for dark matter, improving amplitude calculations and establishing bounds on particle parameters for relic abundance consistency.

Contribution

It introduces an improved method for partial-wave amplitude calculations that satisfy the optical theorem in strongly interacting dark pion models.

Findings

Improved amplitude calculations relevant for semi-relativistic pions.

No impact on cosmic structure self-scattering cross sections.

Upper bound on pion mass for achieving correct relic abundance.

Abstract

Dark pion is a promising candidate for the strongly interacting massive particle dark matter. A large pion self-coupling $m_\pi/f_\pi$ tends to be required for correct relic abundance, and hence the partial-wave amplitudes can violate the perturbative unitarity even for the coupling within na\"ive perturbative regime. We improve the partial-wave amplitudes in order to satisfy the optical theorem. We demonstrate that the improvement is relevant only for semi-relativistic pions, and thus this does not affect the self-scattering cross section at the cosmic structures. We also discuss the impact of the improvement of the $\pi \pi \pi \to \pi \pi$ scattering process, and we find that there is an upper bound on $m_\pi$ at which the correct relic abundance is never achieved even at large $m_\pi/f_\pi$ due to the optical theorem.