The one-loop and Sommerfeld electroweak corrections to the Wino dark matter annihilation

We compute the present-day Wino dark matter annihilation cross-section including the one-loop radiative corrections together with the fully treated electroweak Sommerfeld effect. We discuss what is the consistent way of incorporating these two corrections simultaneously and why simply using the running coupling constants values at the Wino mass scale is not correct. The results show that up to a few TeV scale the full one-loop computation makes the cross-section smaller up to about 30% with respect to the Sommerfeld enhanced tree level result and are considerably larger than the tree or one-loop level without the Sommerfeld effect.