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Near a critical value of the wino mass where there is a zero-energy S-waveresonance at the neutral-wino-pair threshold, low-energy winos can be describedby a zero-range effective field theory (ZREFT) in which the winos interactnonperturbatively through a contact interaction and through Coulombinteractions. The effects of wino-pair annihilation into electroweak gaugebosons are taken into account through the analytic continuation of the realparameters for the contact interaction to complex values. The parameters ofZREFT can be determined by matching wino-wino scattering amplitudes calculatedby solving the Schr\"odinger equation for winos interacting through a realpotential due to the exchange of electroweak gauge bosons and an imaginarypotential due to wino-pair annihilation into electroweak gauge bosons. ZREFT atleading order gives an accurate analytic description of low-energy wino-winoscattering, inclusive wino-pair annihilation, and a wino-pair bound state.ZREFT can also be applied to partial annihilation rates, such as the Sommerfeldenhancement of the annihilation rate of wino pairs into monochromatic photons.

Zero-Range Effective Field Theory for Resonant Wino Dark Matter III. Annihilation Effects