Zero-Range Effective Field Theory for Resonant Wino Dark Matter I. Framework

Understand

The most dramatic "Sommerfeld enhancements" of neutral-wino-pair annihilation occur when the wino mass is near a critical value where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold.

• Near such a critical mass, low-energy winos can be described by a zero-range effective field theory in which the winos interact nonperturbatively through a contact interaction.
• The effective field theory is controlled by a renormalization-group fixed point at which the neutral and charged winos are degenerate in mass and their scattering length is infinite.
• The parameters of the zero-range effective field theory can be determined by matching wino-wino scattering amplitudes calculated by solving the Schr\"odinger equation for winos interacting through a potential due to the exchange of weak gauge bosons.