QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime

TL;DR

This paper extends analytic calculations of parton splitting and joining rates in a quark-gluon plasma to next-to-leading-log order in the high-energy limit, improving accuracy and including running coupling effects.

Contribution

It provides the first next-to-leading-log analytic calculations of QCD splitting/joining functions at finite temperature in the LPM regime, aligning well with numerical results.

Findings

Agreement within 20% for E ≥ 10 T

Extension to next-to-leading-log order

Inclusion of running coupling effects

Abstract

There exist full leading-order-in-alpha_s numerical calculations of the rates for massless quarks and gluons to split and join in the background of a quark-gluon plasma through hard, nearly collinear bremsstrahlung and inverse bremsstrahlung. In the limit of partons with very high energy E, where the physics is dominated by the Landau-Pomeranchuk-Migdal (LPM) effect, there are also analytic leading-log calculations of these rates, where the logarithm is ln(E/T). We extend those analytic calculations to next-to-leading-log order. We find agreement with the full result to within roughly 20% for E(less) >~ 10 T, where E(less) is the energy of the least energetic parton in the splitting/joining process. We also discuss how to account for the running of the coupling constant in the case that E/T is very large. Our results are also applicable to isotropic non-equilibrium plasmas if the plasma does not change significantly over the formation time associated with particle splitting.