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The mass of primordial dark matter (DM) protohalos remains unknown. However,the missing satellites problem may be an indication that they are quite large.In this paper, we use effective field theory to map constraints on darkmatter-SM interactions into limits on the mass of DM protohalos. Given thatleptons remain in the thermal bath until late times, we focus on theirinteractions with DM. To illustrate the method, we use the null results of LEPmissing energy searches along with Fermi-LAT searches for DM annihilation innearby dwarf galaxies, to derive limits on the protohalo mass, $\lesssim(10^{-6}-10^{-1}) M_{\odot}$, with the range depending on the DM mass and theoperator. Thus, if DM is to remain thermally coupled until late times andaccount for the missing satellites, charged lepton interactions areinsufficient. This motivates neutrinophilic DM, which can have protohalo massesorders of magnitude larger, with constraints arising from Planck, IceCube andunpublished Super-K data. We show that effective neutrinophilic models offer asolution to the missing satellites problem for sub-GeV DM masses with largerthan WIMP-sized annihilation cross sections.

Constraints on Dark Matter Protohalos in Effective Theories and Neutrinophilic Dark Matter