Sommerfeld Effect and Bound State Formation for Dark Matter Models with Colored Mediators with SE+BSF4DM

TL;DR

We address how non-perturbative long-range QCD effects modify the relic density and experimental constraints in four simplified $t$-channel DM models with colored mediators near mass degeneracy. We develop a comprehensive formalism for Sommerfeld enhancement and bound-state formation, including excited bound states up to $n=6$, and implement it as SE+BSF4DM in micrOMEGAs, enabling automated relic-density calculations for generic DMSimpt models. Parameter scans across $m_{\text{DM}}$, $\Delta m$, and $g_{\text{DM}}$ show that SE+BSF can shift the required coupling by ${\cal O}(1)$ and substantially widen the viable parameter space, with notable implications for direct detection and LHC bound-state searches. Overall, the work demonstrates the crucial role of non-perturbative effects in thermal DM scenarios with colored coannihilation partners and provides a ready-to-use tool for precise phenomenology.

Abstract

In the universal framework of simplified $t$-channel dark matter models, the calculation of the relic abundance can be dominated by mediator annihilation when the dark matter and mediator masses are almost degenerate. We analyze four representative models with scalar and fermionic mediators, confront them with direct detection limits and highlight the differences and common features between them. The mediator annihilations are considerably enhanced by the Sommerfeld effect and bound state formation. Albeit their effect is subdominant in the coannihilation regime, excited bound state levels are included as well. We find that Sommerfeld and bound-state effects can lead to order one corrections to the constraints on the DM mass in the coannihilating regime, with the precise magnitude depending on the specific model realization. In addition we provide SE+BSF4DM, an intuitive and easy to use add-on to micrOMEGAs, allowing for an automated inclusion of these effects for a generic $t$-channel Dark Matter Model, which is publicly available on Github.

Figures (8)

• Figure 1: Diagrammatic illustration of radiative bound state formation. The labels $X^{(\dagger)}$ for the incoming legs indicate $X^\dagger-X^\dagger$, $X^\dagger-X$ and $X-X$ BSF. From Ref. Becker:2022iso.
• Figure 2: Mass splitting $\Delta m$ vs. DM mass $m_\text{DM}$ for the four models considered. Blue (yellow) bands correspond to a $5 \sigma$ uncertainty of $\Omega h^2$Planck:2018vyg for $g_\text{DM} = 1$ ($10^{-2}$). Dash-dotted bands correspond to the conventional perturbative calculation, dashed bands include the Sommerfeld effect. Bound state formation for the ground state ($n = 1$) is indicated by the dotted lines, which in most of parameter space overlay with the solid bands for $n = 6$.
• Figure 4: Representative Feynman diagrams corresponding to the main processes contributing to (co-)annihilations. From Ref. Becker:2022iso.
• Figure 5: Experimental bounds on the S3M models with Majorana Dark Matter and a complex scalar mediator. The upper row is for the models coupling to the up-quark, the lower for couplings to the top. The left column shows the constraints without long-range effects, while the right column includes them.
• Figure 6: Same as Fig. \ref{['fig:Money_plots_S3M']}, but plotted on a linear Dark Matter mass axis. Experimental bounds on the S3M model with Majorana Dark Matter and a complex scalar mediator, showing couplings to up quarks (upper row) and top quarks (lower row), without (left) and with (right) long-range effects.