Breit-Wigner enhancement considering the dark matter kinetic decoupling

Abstract

In this paper we study the Breit-Wigner enhancement of dark matter (DM) annihilation considering the kinetic decoupling in the evolution of DM freeze-out at the early Universe. Since the DM temperature decreases much faster (as $1/{R}^{2}$) after kinetic decoupling than that in kinetic equilibrium (as $1/R$), we find the Breit-Wigner enhancement of the DM annihilation rate after the kinetic decoupling will affect the DM relic density significantly. Focusing on the model parameters that try to explain the anomalous cosmic positron/electron excesses observed by PAMELA/Fermi/ATIC, we find the elastic scattering $Xf\ensuremath{\rightarrow}Xf$ is not efficient in keeping dark matter in kinetic equilibrium, and the kinetic decoupling temperature ${T}_{\mathrm{kd}}$ is comparable to the chemical decoupling temperature ${T}_{f}\ensuremath{\sim}O(10)\text{ }\text{ }\mathrm{GeV}$. The reduction of the relic density after ${T}_{\mathrm{kd}}$ is significant and leads to a limited enhancement factor $\ensuremath{\sim}O({10}^{2})$. Therefore, it is difficult to explain the anomalous positron/electron excesses in cosmic rays by DM annihilation and give the correct DM relic density simultaneously in the minimal Breit-Wigner enhancement model. We also mention that if the nonthermal DM velocity distribution after kinetic decoupling or new scattering processes are considered, this constraint could be changed.