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.
Highlights
Pairs of heavy particles inside a relativistic plasma are intriguing systems from both theoretical and experimental points of view
Nc is the number of “colors” of the gauge group SU(Nc). These next-leading order (NLO) results are valid for any singlet-adjoint or adjoint-singlet transition for both quarkonium and dark matter (DM)
In the hierarchy M v T, it encodes all essential information of the non-Alelian plasma that determines the heavy particle bound state dissociation and formation rates that appear in the Boltzmann and rate equations for quarkonium transport in the quark-gluon plasma (QGP) and DM bound state formation in the early universe
Summary
Pairs of heavy particles inside a relativistic plasma are intriguing systems from both theoretical and experimental points of view. Where Ei is the (non-Abelian) electric field with the spatial index i = 1, 2, 3, the subscript T is the temperature and indicates the expectation value is taken at thermal equilibrium, W represents a path-ordered Wilson line in the adjoint representation, and a, b are color indices that are summed over At this stage, we would like to emphasize that the correlator in eq (1.1) for bound state formation and dissociation is different from the well-studied electric field correlator for the heavy quark diffusion coefficient [74–77], Trcolor [U (−∞, t)Ei(t)U (t, 0)Ei(0)U (0, −∞)] T ,.
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