Rapid thermal co-annihilation through bound states in QCD

The co-annihilation rate of heavy particles close to thermal equilibrium, which plays a role in many classic dark matter scenarios, can be simulated in QCD by considering the pair annihilation rate of a heavy quark and antiquark at a temperature of a few hundred MeV. We show that the so-called Sommerfeld factors, parameterizing the rate, can be defined and measured non-perturbatively within the NRQCD framework. Lattice measurements indicate a modest suppression in the octet channel, in reasonable agreement with perturbation theory, and a large enhancement in the singlet channel, much above the perturbative prediction. The additional enhancement is suggested to originate from bound state formation and subsequent decay. Making use of a Green's function based method to incorporate thermal corrections in perturbative co-annihilation rate computations, we show that qualitative agreement with lattice data can be found once thermally broadened bound states are accounted for. We suggest that our formalism may also be applicable to specific dark matter models which have complicated bound state structures.