Non-perturbative Effect on Thermal Relic Abundance of Dark Matter

TL;DR

The paper investigates how non-perturbative Sommerfeld enhancement, arising from long-range SU(2)_L interactions, alters the thermal relic abundance of heavy dark matter that is non-singlet under SU(2)_L. It develops a two-body effective Lagrangian to compute Sommerfeld-enhanced annihilation cross sections and solves the Boltzmann equation including coannihilation effects. For a wino-like neutralino, the enhancement increases annihilation rates at freeze-out, reducing the relic abundance by about 50% and shifting the WMAP-compatible mass to approximately 2.7–3.0 TeV. These results emphasize the importance of non-perturbative effects in precise relic-density predictions and imply similar corrections for other SU(2)_L charged DM candidates, though the magnitude can vary with representation (e.g., ~10% for higgsinos).

Abstract

We point out that thermal relic abundance of the dark matter is strongly altered by a non-perturbative effect called the Sommerfeld enhancement, when constituent particles of the dark matter are non-singlet under the SU(2)_L gauge interaction and much heavier than the weak gauge bosons. Typical candidates for such dark matter particles are the heavy wino- and higgsino-like neutralinos. We investigate the non-perturbative effect on the relic abundance of dark matter for the wino-like neutralino as an example. We show that its thermal abundance is reduced by 50% compared to the perturbative result. The wino-like neutralino mass consistent with the observed dark matter abundance turns out to be 2.7 TeV < m < 3.0 TeV.

Figures (2)

• Figure 1: Mass dependence of averaged cross section, $\langle \sigma_{\rm eff} \rangle$, normalized by the perturbative one, $\langle \sigma_{\rm eff} \rangle_{\rm Tree}$, for $m/T = 20,~200,~2000$ (left figure), and temperature dependence with $m = 2.8$ TeV (right figure). The perturbative result is also shown as a dotted line for comparison. Here, mass difference between $\tilde{\chi}^0$ and $\tilde{\chi}^\pm$ is $\delta m \simeq$ 0.17 GeV.
• Figure 2: Ratio of yield with the non-perturbative effect to that in the perturbative calculation (left figure). Wino-like neutralino mass is fixed 2.8 TeV. Thermal relic abundance of the dark matter in the current universe as a function of wino-like neutralino mass (right figure). Allowed regions by the WMAP at 1(2) $\sigma$ levels are also shown as the dark (light) shaded area.