Inelastic dark matter, small scale problems, and the XENON1T excess

We study a generic model in which the dark sector is composed of a Majorana dark matter $\chi_1$, its excited state $\chi_2$, both at the electroweak scale, and a light dark photon $Z'$ with $m_{Z'} \sim 10^{-4}$ eV. The light $Z'$ enhances the self-scattering elastic cross section $\chi_1 \chi_1 \to \chi_1 \chi_1$ enough to solve the small scale problems in the $N$-body simulations with the cold dark matter. The dark matter communicates with the SM via kinetic mixing parameterized by $\epsilon$. The inelastic scattering process $\chi_1 \chi_1 \to \chi_2 \chi_2$ followed by the prompt decay $\chi_2 \to \chi_1 Z'$ generates energetic $Z'$. By setting $\delta \equiv m_{\chi_2} - m_{\chi_1} \simeq 2.8$ keV and $\epsilon \sim 10^{-10}$ the excess in the electron-recoil data at the XENON1T experiment can be explained by the dark-photoelectric effect. The relic abundance of the dark matter can also be accommodated by the thermal freeze-out mechanism via the annihilation $\chi_1 \chi_1 (\chi_2 \chi_2) \to Z' Z'$ with the dark gauge coupling constant $\alpha_X \sim 10^{-3}$.