Electrophilic dark matter with dark photon: from DAMPE to direct detection

The electron-positron excess reported by the DAMPE collaboration recently may be explained by an electrophilic dark matter (DM). A standard model singlet fermion may play the role of such a DM when it is stablized by some symmetries, such as a dark $U(1)_X^{}$ gauge symmetry, and dominantly annihilates into the electron-positron pairs through the exchange of a scalar mediator. The model, with appropriate Yukawa couplings, can well interpret the DAMPE excess. Naively one expects that in this type of models the DM-nucleon cross section should be small since there is no tree-level DM-quark interactions. We however find that at one-loop level, a testable DM-nucleon cross section can be induced for providing ways to test the electrophilic model. We also find that a $U(1)$ kinetic mixing can generate a sizable DM-nucleon cross section although the $U(1)_X^{}$ dark photon only has a negligible contribution to the DM annihilation. Depending on the signs of the mixing parameter, the dark photon can enhance/reduce the one-loop induced DM-nucleon cross section.