Manual for SE+BSF4DM -- A micrOMEGAs package for Sommerfeld Effect and Bound State Formation in colored Dark Sectors

TL;DR

SE+BSF4DM addresses the challenge of accurately predicting the dark matter relic density in models with strong dark-sector interactions by embedding non-perturbative effects—Sommerfeld enhancement and bound-state formation—into the micrOMEGAs framework for $SU(3)_c$-charged particles. The method extracts the $s$-wave component of colored annihilations and applies color-decomposed Sommerfeld factors, while automatically accounting for bound-state formation and their transitions, decays, and ionizations using literature rates. The package offers a modular, user-friendly workflow with configurable BSF schemes (No Transition, Efficient Transition, Ionization Equilibrium, Full Matrix) and supports multiple benchmark $t$-channel models, enabling on-the-fly, robust relic-density calculations. It highlights performance trade-offs, underlines the assumption of chemical equilibrium in the dark sector, and outlines future directions such as conversion-driven freeze-out and extensions to other color representations, ultimately enabling more precise phenomenology of colored dark sectors.

Abstract

This manual describes the usage and implementation of SE+BSF4DM, an add-on package for micrOMEGAs that includes the Sommerfeld effect and bound state formation in the numerical evaluation of the dark matter relic density for QCD-colored dark sectors, applicable to any model that can be mapped onto a simplified t-channel framework. The package seamlessly integrates these non-perturbative effects into the standard micrOMEGAs workflow, requiring minimal user modification. This document provides a comprehensive guide to the installation, configuration, and usage of SE+BSF4DM, serving as a practical user guide for dark matter phenomenologists.

Figures (4)

• Figure 1: Schematic workflow of the SE+BSF4DM package.
• Figure 2: Schematic BSF process with ionization, decay, and transitions.
• Figure 3: Comparison of effective cross sections for different bound-state treatment methods in the F3SuR model with mass degenerate dark sector particles $m_X = m_Y = 1$ TeV and a $t-$channel coupling $\lambda = 0.01$. All black lines are computed including $n = 15$ bound states according to the four methods discussed in the main text. Colors indicate contributions from different principal quantum numbers $n$ using the full matrix solution.
• Figure 4: Dependence of the bound-state enhanced cross section on mass splitting $\delta$ in the F3SuR model for a DM mass $m_X = 1$ TeV, a $t$-channel coupling $\lambda = 0.01$ and including SE and $n = 15$ bound states using the Full Matrix method. Smaller splittings allow longer-lived co-annihilation, enhancing late-time bound-state formation.