P-wave Sommerfeld enhancement near threshold: a simplified approach

TL;DR

This paper introduces a simplified method to compute the P-wave Sommerfeld enhancement near threshold, focusing on resonant contributions and avoiding divergences without needing full non-resonant calculations.

Contribution

It provides a new prescription for calculating finite P-wave Sommerfeld enhancement in the narrow-width approximation, simplifying the treatment of unstable particles near threshold.

Findings

The method eliminates divergences in P-wave enhancement calculations.

It allows for a finite resonant contribution without non-resonant processes.

The approach is similar to the standard S-wave Sommerfeld enhancement.

Abstract

The calculation of P-wave Sommerfeld enhancement in processes with unstable particles in the final state is known to be divergent. In a complete description, where resonant (on-shell unstable particles) and non-resonant contributions are included, it has been shown that results are finite. For most beyond the Standard Model applications, these complete calculations are not readily available. In this work, we are interested in the near-threshold region and we consider only the resonant contribution. In this case, we provide a simplified prescription to compute the P-wave Sommerfeld enhancement in the narrow-width approximation of the unstable particle that directly eliminates divergences. We show that we can define a finite resonant contribution without the inclusion of the non-resonant processes in a way similar to the usual S-wave Sommerfeld enhancement.