# Electroweak and Higgs Boson Internal Bremsstrahlung: General considerations for Majorana dark matter annihilation and application to MSSM neutralinos

## TL;DR

This paper analyzes how internal bremsstrahlung can lift helicity suppression in Majorana dark matter annihilation, especially in MSSM neutralinos, leading to enhanced rates and altered spectra relevant for indirect detection.

## Contribution

It provides a comprehensive analytical calculation of neutralino annihilation amplitudes with additional bosons, classifies scenarios with large three-body rates, and emphasizes correct treatment of spectra for indirect detection.

## Key findings

- Enhanced annihilation rates due to bremsstrahlung effects.
- Significant differences in predicted spectra for indirect detection.
- Identification of previously overlooked cases with large three-body contributions.

## Abstract

It is well known that the annihilation of Majorana dark matter into fermions is helicity suppressed. Here, we point out that the underlying mechanism is a subtle combination of two distinct effects, and we present a comprehensive analysis of how the suppression can be partially or fully lifted by the internal bremsstrahlung of an additional boson in the final state. As a concrete illustration, we compute analytically the full amplitudes and annihilation rates of supersymmetric neutralinos to final states that contain any combination of two standard model fermions, plus one electroweak gauge boson or one of the five physical Higgs bosons that appear in the minimal supersymmetric standard model. We classify the various ways in which these three-body rates can be large compared to the two-body rates, identifying cases that have not been pointed out before. In our analysis, we put special emphasis on how to avoid the double counting of identical kinematic situations that appear for two-body and three-body final states, in particular on how to correctly treat differential rates and the spectrum of the resulting stable particles that is relevant for indirect dark matter searches. We find that both the total annihilation rates and the yields can be significantly enhanced when taking into account the corrections computed here, in particular for models with somewhat small annihilation rates at tree-level which otherwise would not be testable with indirect dark matter searches. Even more importantly, however, we find that the resulting annihilation spectra of positrons, neutrinos, gamma-rays and antiprotons differ in general substantially from the model-independent spectra that are commonly adopted, for these final states, when constraining particle dark matter with indirect detection experiments.