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

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 dark matter-SM interactions into limits on the mass of DM protohalos. Given that leptons remain in the thermal bath until late times, we focus on their interactions with DM. To illustrate the method, we use the null results of LEP missing energy searches along with Fermi-LAT searches for DM annihilation in nearby 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 the operator. Thus, if DM is to remain thermally coupled until late times and account for the missing satellites, charged lepton interactions are insufficient. This motivates neutrinophilic DM, which can have protohalo masses orders of magnitude larger, with constraints arising from Planck, IceCube and unpublished Super-K data. We show that effective neutrinophilic models offer a solution to the missing satellites problem for sub-GeV DM masses with larger than WIMP-sized annihilation cross sections.