Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport

TL;DR

This paper presents a comprehensive NLO calculation of the non-Abelian electric field correlator in a plasma, relevant for understanding heavy particle bound states and dark matter interactions in thermal environments.

Contribution

It provides the first complete NLO computation of the electric field correlator in a non-Abelian plasma, including gauge independence and renormalization group analysis.

Findings

Gauge-independent results confirmed in R_xi gauge

Explicit NLO expressions for electric field correlator

Applicability to quarkonium dissociation and dark matter interactions

Abstract

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU($N_c$) 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 $R_\xi$ 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.