We derive bounds on the dark matter annihilation cross-section for low-mass (5--20 GeV) dark matter annihilating primarily to up or down quarks, using the Fermi-LAT bound on gamma-rays from Milky Way satellites. For models in which dark matter-Standard Model interactions are mediated by particular contact operators, we show that these bounds can be directly translated into bounds on the dark matter-proton scattering cross section. For isospin-violating dark matter, these constraints are tight enough to begin to constrain the parameter-space consistent with experimental signals of low-mass dark matter. We discuss possible models that can evade these bounds.
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Kumar et al. (2012) studied this question.
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