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Universal Two-body Physics in Dark Matter near an S-wave Resonance

The dark matter annihilation rate at small relative velocities can be amplified by a large boost factor using various mechanisms, including Sommerfeld enhancement, resonance enhancement, and Breit-Wigner enhancement. These mechanisms all involve a resonance near the threshold for a pair of dark matter particles. We point out that if the resonance is in the S-wave channel, the mechanisms are equivalent sufficiently near the resonance and they are constrained by universal two-body physics. The amplified annihilation rate requires a corresponding amplification of the elastic scattering cross section. If the resonance is a bound state below the threshold, it has an increased lifetime that is inversely proportional to the square root of the binding energy. Its spatial structure is that of two dark matter particles whose mean separation is also inversely proportional to the square root of the binding energy.