Effect of thermal fluctuations on dark matter annihilation cross section

We are interested in thermal corrections to dark matter (DM) annihilation cross sections in a MSSM-inspired BSM theory, having bino-like Majorana DM ($\chi$), annihilating to SM fermions through Yukawa interactions via a charged scalar channel in freeze-out scenario. We apply real-time formalism of thermal field theory (TFT) to investigate corrections due to thermal fluctuations of DM annihilation cross section at NLO. We utilize generalized Grammer and Yennie approach in TFT to assure IR divergence cancellation between K-photon of virtual and $\widetilde{K}$-photon of real corrections at NLO to DM annihilation processes ($\chi \bar{\chi} \to f \bar{f}$). We calculate the thermal correction to the finite remainder in TFT. Our calculations shows quadratic thermal dependence of annihilation cross section of DM ($ \sigma_T \sim \mathcal{O}(T^2) $) considering scalar to be heavy compared to DM and SM fermions.