Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport

Abstract

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(Nc) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the Rξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

Bound-state effects on dark matter coannihilation: Pushing the boundaries of conversion-driven freeze-out

“…For the 1s ground state our result agrees with [26], and for the 2s state with [29,30]. The result for 2p differs from the one given in [29,30] (by a factor 3 for the s-wave contribution with = 0, and a factor 3/2 for the d-wave with = 2, but matches the result for hydrogen when translated to the electromagnetic case [36].…”

“…In this region, the zerotemperature correction dominates. This is the reason why the difference between LO and the NLO correction considered in [30] is moderate in the right part of the left panel in Fig. 9.…”

“…/s] FIG. 9: Impact of the class of NLO corrections presented in [30] on the contribution to the effective cross section, eq. ( 25), from bound states.…”

“…We leave an exploration of the full result including transitions to future work, and use the no-transition limit with n ≤ 15 as default choice in the following. For a discussion of the impact of a certain class of higher order corrections (related to collisional ionization and recombination processes and the associated virtual contributions) computed in [27,30] as well as to…”

“…[28,29]). Recently, next-to-leading order finite temperature corrections of the general singletadjoint dipole interactions have been computed [30].…”