  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.
