Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach

Tobias Binder,Kyohei Mukaida,Burkhard Blobel,Julia Harz

doi:10.1007/jhep09(2020)086

Abstract

The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel. The amplitudes for those higher-order processes, however, are divergent in the collinear direction of the in- and out-going bath particles if the mediator is massless. To address the issue of collinear divergences, we derive the bound-state formation collision term in the framework of non-equilibrium quantum field theory. The main result is an expression for a more general cross section, which allows to compute higher-order bound-state formation processes inside the primordial plasma background in a comprehensive manner. Based on this result, we show that next-to-leading order contributions, including the bath-particle scattering, are i) collinear finite and ii) generically dominate over the on-shell emission for temperatures larger than the absolute value of the binding energy. Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios.

Highlights

One famous example in the Minimal Supersymmetric extension of the SM (MSSM) is the traditional case of wino-like neutralino, for which the important role of quantum mechanical effects was pointed out in seminal works [5,6,7,8]
The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel
Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios

Summary

Introduction

One famous example in the Minimal Supersymmetric extension of the SM (MSSM) is the traditional case of wino-like neutralino, for which the important role of quantum mechanical effects was pointed out in seminal works [5,6,7,8]. Already at the TeV mass region, the ladder exchange of the most massive SM gauge bosons enhances the probability that a slowly moving wino pair annihilates This quantum mechanical effect is called Sommerfeld enhancement (SE) [9] or Sakharov enhancement [10] and lowers the predicted abundance by about 50 % compared to a tree-level computation in this case [8]. Coannihilation examples are illustrated diagrammatically, where the charged coannihilating partner can form bound states via SM bath-particle scattering through the exchange of a photon or gluon Since they all come with a large multiplicity, one may ask the question by how much these additional processes contribute to the previously studied case of BSF via the emission of an on-shell mediator only. The question by how much these processes could deplete the DM relic abundance can not be answered given the conventional methods

Objectives

Discussion

Conclusion