  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. If the wino mass is larger than the critical
value, the resonance is a wino-pair bound state. The power of the zero-range
effective field theory is illustrated by calculating the rate for formation of
the bound state in the collision of two neutral winos through the emission of
two soft photons.
