Dark Parton Shower Effects for Cosmic Ray Boosted Dark Matter

We investigate the dark parton shower effects in the direct detection of cosmic-ray boosted dark matter (CRDM), focusing on a dark photon-mediated model with fermionic dark matter-electron interactions. Utilizing a Monte Carlo framework to incorporate the Sudakov form factors and kinematic dipole recoil schemes, we simulate the CRDM energy spectrum evolution under the dark sector splitting. Our results reveal a significant energy-dependent modification of the CRDM flux. For a 1 keV dark matter (DM) mass and a coupling of $g_D=3$, the CRDM flux can be enhanced by a factor up to 1.12 in the $\mathcal{O}(10^{-2} \sim 1)$ MeV energy range for $2m_\chi \lesssim m_{A^\prime} \lesssim 10^{-2}$ MeV, while it is suppressed by more than $50\%$ at energy around 100 MeV for $m_{A^\prime} \lesssim 10^{-3}$ MeV. We then translate these effects into the experimental sensitivities for PandaX-4T, Super-Kamiokande, and JUNO. At $m_{A^\prime} = 10^{-3}$ MeV and $g_D=3$, the bounds on the kinetic mixing parameter $\epsilon^2$ are relaxed by factors of 1.02, 1.6 and 1.4, respectively. Finally, we demonstrate that the parameter space considered is consistent with those astrophysical constraints on dark matter self-interactions from observations of the Bullet Cluster.