The Damping of Energetic Gluons and Quarks in High-Temperature QCD

TL;DR

This paper derives the damping rates of energetic gluons and quarks in high-temperature QCD plasma, providing simple arguments to determine the numerical coefficients and clarifying the perturbative limitations.

Contribution

It introduces a straightforward method to fix the damping rate coefficients and shows the incalculability of higher-order terms without additional assumptions.

Findings

Damping rate for gluons: c_g = C_a / (4π)

Damping rate for quarks: c_q = C_f / (4π)

Results agree with some previous detailed calculations

Abstract

When a gluon or a quark is sent through the hot QCD plasma it can be absorbed into the ambient heat bath and so can acquire an effective lifetime. At high temperatures and for weak couplings the inverse lifetime, or damping rate, for energetic quarks and transverse gluons, (those whose momenta satisfy $|\p| \gg gT$) is given by $\gamma(\p) = c\; g^2 \log\left({1\over g}\right)\; T + O(g^2T)$. We show that very simple arguments suffice both to fix the numerical coefficient, $c$, in this expression and to show that the $O(g^2T)$ contribution is incalculable in perturbation theory without further assumptions. For QCD with $N_c$ colours we find (expressed in terms of the casimir invariants $C_a=N_c$ and $C_f=(N_c^2-1)/(2N_c)$): $c_g=+{C_a\over 4\pi}$ for gluons and $c_q=+{C_f\over 4\pi}$ for quarks. These numbers agree with the more detailed calculations of Pisarski \etal\ but disagree with those of Lebedev and Smilga. The simplicity of the calculation also permits a direct verification of the gauge-invariance and physical sign of the result.