We show that the presence of nearby Coulombic resonances at finite energy could lead to the enhancement of the dark matter annihilation cross section at specific non-zero velocities correlated with the mass splitting between the dark matter pair and that of the resonance. If one of these resonant velocities approximately matches the velocity of dark matter in our local neighbourhood, we would see this enhancement in existing indirect-detection measurements, such as the measurements of the continuum photon spectrum made by HESS and Fermi-LAT. We explore this effect in the context of pure Higgsino and Wino dark matter with a variable splitting between charged and neutral components, controlled by the Wilson coefficient of a higher-dimension operator. For electroweak WIMPs a relevant and appreciable enhancement from Coulomb resonances requires tuning the charged-neutral splitting to be of order the Coulomb binding energies. This leads to strong exclusions of Higgsino dark matter with charged-neutral splittings in the narrow ranges (2, 2.5) and (8.5, 10.5) MeV. In contrast, by decreasing the charged-neutral splitting for the thermal Wino, we can move the Yukawa resonance away from the thermal relic mass, decreasing the indirect-detection signal to a level that is compatible with HESS measurements in the window (25, 35) MeV.
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