Effective field theory for resonant wino dark matter

Enhancements in WIMP annihilation rates have been identified with a nonperturbative "Sommerfeld enhancement" arising from the exchange of light mediators. At certain critical values of the WIMP mass, the enhancement is increased dramatically due to a zero-energy resonance at the WIMP-pair threshold. For masses near these critical values, WIMP scattering processes are accurately described by an effective field theory where WIMPs have nonperturbative zero-range contact interactions. The effective field theory is controlled by a renormalization-group fixed point at which the WIMPs are degenerate in mass and their scattering length is infinite. If the WIMPs can exchange massless mediators, the resulting long-range interaction must also be treated nonperturbatively. We develop an effective field theory for SU(2)-triplet dark matter, which have short-range weak and long-range electromagnetic interactions. We refer to these dark matter particles as winos. The long-range Coulomb interaction between charged winos is resummed to all orders. The parameters of the effective field theory can be determined by matching wino-wino scattering amplitudes calculated by solving the Schr\"odinger equation with a potential describing exchange of electroweak gauge bosons. With Coulomb resummation, the effective field theory at leading order gives a good description of the low-energy two-body observables for winos.