Collision Rate and Symmetry Factor in Gluon Plasma

TL;DR

This paper calculates collision rates in a gluon plasma, analyzing symmetry factors and phase space integrals, demonstrating their equivalence through analytic and numerical methods for specific gluon processes.

Contribution

It provides a detailed comparison of symmetry factor inclusion versus full phase space integration in gluon collision calculations, showing their equivalence.

Findings

Symmetry factor and phase space integral yield equivalent results.

Analytic and numerical methods confirm the equivalence for $gg \rightarrow gg$ and $gg \rightarrow ggg$ processes.

Clarifies the role of symmetry factors in gluon collision rate calculations.

Abstract

The elastic and inelastic collision rates in a gluon gas are calculated. The symmetry factor and the phase space integral are discussed in detail. With a symmetry factor and well constrained phase space, the same result can be obtained as that of the full phase space without the factor. Such an equivalence is illustrated by analytic and numerical calculations for $gg \rightarrow gg$ and $gg\rightarrow ggg$ processes.