Rapid thermal co-annihilation through bound states in QCD

TL;DR

This paper investigates the co-annihilation rates of heavy particles in QCD using lattice and perturbative methods, revealing significant bound state effects that could inform dark matter models.

Contribution

It introduces a non-perturbative framework for defining and measuring Sommerfeld factors in QCD, highlighting the impact of bound states on co-annihilation rates.

Findings

Lattice results show a large enhancement in the singlet channel due to bound states.

Modest suppression observed in the octet channel aligns with perturbative predictions.

Thermal broadening of bound states improves agreement between lattice data and perturbative calculations.

Abstract

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.