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Probing sub-GeV leptophilic dark matter at Belle II and NA64

An analysis is given of the Belle II sensitivities and NA64 constraints on the sub-GeV Dirac dark matter that interacts with charged leptons. We consider two different types of interactions between sub-GeV Dirac dark matter and the charged leptons: the EFT operators and the light vector mediators. We compute the Belle II mono-photon sensitivities on sub-GeV dark matter with 50 ab$^{-1}$ data which are expected to be accumulated in the full Belle II runs. Although the Belle II mono-photon sensitivities on the EFT operators are of similar size as the LEP constraints, Belle II can probe new parameter space of the light vector mediator models that are unexplored by LEP. For both the EFT operators and the light vector mediator models, the Belle II mono-photon sensitivities can be several orders of magnitude stronger than the current dark matter direct detection limits, as well as the white dwarf limits. The light vector mediator can also be directly searched for by reconstructing the invariant mass of its di-lepton decay final states at Belle II, which is found to be complementary to the mono-photon channel. We compute the NA64 constraints on the sub-GeV Dirac dark matter and provide analytic expressions of the dark matter cross section in the Weizsäcker-Williams approximation, for the EFT operators, and for the light vector mediator models. We find that the current NA64 data (with $2.84 \times 10^{11}$ electron-on-target events) provide strong constraints on sub-GeV dark matter. Although the NA64 constraints are found to be about one order of magnitude smaller than the Belle II sensitivities for the EFT operators, NA64 can probe some regions of the parameter space in the light vector mediator models that are beyond the reach of Belle II.