Breit-Wigner Enhancement Considering the Dark Matter Kinetic Decoupling

In the 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 DM annihilation rate after the kinetic decoupling will affect the DM relic density significantly. Focusing on the model parameters that trying to explain the anomalous cosmic positron/electron excesses observed by PAMELA/Fermi/ATIC we find the elastic scattering $Xf\to Xf$ is not efficient to keep dark matter in kinetic equilibrium, and the kinetic decoupling temperature $T_{kd}$ is comparable to the chemical decoupling temperature $T_f\sim O(10) GeV$. The reduction of the relic density after $T_{kd}$ is significant and leads to a limited enhancement factor $\sim O(10^2)$. 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.