Sommerfeld effect in heavy quark chemical equilibration

TL;DR

This paper investigates how the Sommerfeld effect influences heavy quark chemical equilibration in a quark-gluon plasma, revealing significant enhancement in the singlet channel but a small overall impact on the rate.

Contribution

It provides the first calculation of the leading-order heavy quark equilibration rate below the quark mass scale, incorporating the Sommerfeld effect into the analysis.

Findings

Large enhancement in the singlet channel due to the Sommerfeld effect.

Total equilibration rate remains small because the octet channel dominates.

Demonstrates incorporation of non-relativistic QCD operators into the imaginary-time formalism.

Abstract

The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T < alphas^2 M. We compute the leading-order equilibration rate in this regime; there is a large enhancement in the singlet channel, but the rate is dominated by the octet channel, and therefore the total effect is small. In the course of the computation we demonstrate how operators that represent the annihilation of heavy quarks in non-relativistic QCD can be incorporated into the imaginary-time formalism.