Relic Abundance of Asymmetric Dark Matter

TL;DR

The paper addresses how the relic abundance is produced for asymmetric dark matter (ADM) where $\chi$ and $\bar{\chi}$ are distinct. It solves the coupled Boltzmann equations for $Y_{\chi}$ and $Y_{\bar{\chi}}$ with a conserved asymmetry $C = Y_{\chi} - Y_{\bar{\chi}}$, deriving semi-analytic solutions that depend on the annihilation cross section via $\langle \sigma v \rangle \simeq a + 6 b/x$. The key contributions include analytic expressions for the late-time abundances, a corrected freeze-out temperature, and quantified parameter-space constraints showing that indirect detection signals are suppressed by the asymmetry; large cross sections can be compensated by increasing $C$, reducing today’s annihilation rate by up to $10^5$ and enabling MeV-scale DM scenarios. This work demonstrates that ADM can reproduce the observed relic density while relaxing indirect-detection bounds, broadening viable DM models and informing MeV DM model-building.

Abstract

We investigate the relic abundance of asymmetric Dark Matter particles that were in thermal equilibrium in the early universe. The standard analytic calculation of the symmetric Dark Matter is generalized to the asymmetric case. We calculate the asymmetry required to explain the observed Dark Matter relic abundance as a function of the annihilation cross section. We show that introducing an asymmetry always reduces the indirect detection signal from WIMP annihilation, although it has a larger annihilation cross section than symmetric Dark Matter. This opens new possibilities for the construction of realistic models of MeV Dark Matter.

Figures (6)

• Figure 1: The evolution of the scaled $\chi$ and $\bar{\chi}$ abundances as function of $x=m/T$ for $a=5\times 10^{-9}$ GeV$^{-2}$, $b=0, \ m = 100$ GeV and $C=10^{-11}$ or zero. The $\bar{\chi}$ equilibrium distributions are shown for comparison.
• Figure 2: The relic density $\Omega h^2$ for particle $\chi$ and anti--particle $\bar{\chi}$ as a function of the cross section. Here we take $m_\chi = 100$ GeV, $g_{\chi} = 2$ and $g_* = 90$. Panel (a) is for $b=0$, while panel (b) is for pure $P-$wave annihilation ($a=0$).
• Figure 3: The ratio of the exact value of the $\bar{\chi}$ particle abundance to the analytic value of $\bar{\chi}$ particle abundance.
• Figure 4: The allowed region in the $(a,C)$ plane for $b=0$ (left), and in the $(b,C)$ plane for $a=0$ (right), when the Dark Matter density $\Omega h^2$ lies between 0.10 and 0.12. Here we take $m_\chi = 100$ GeV, $g_{\chi} = 2$ and $g_* = 90$; the allowed values of $C$ scale to good approximation like $1/m_\chi$.
• Figure 5: Ratio of the current anti--particle abundance $Y_{\bar{\chi}}$ to the particle abundance $Y_\chi$ as a function of $m_\chi \cdot C$ (left) or the sum $a + b/6$ characterizing the annihilation cross section (right) for different combinations of cross sections and total Dark Matter relic density. In the left (right) frame the annihilation cross section (asymmetry $C$) is chosen such that the total dark matter density $\Omega_{\rm DM} h^2$ has the indicated value. Results are for $g_*=90$ and $m_\chi = 100$ GeV, but are almost independent of $m_\chi$.