Altarelli-Parisi Equation in Non-Equilibrium QCD

TL;DR

This paper derives non-equilibrium QCD splitting functions using Schwinger-Keldysh formalism, extending the DGLAP evolution to quark-gluon plasma conditions relevant for RHIC and LHC.

Contribution

It introduces a method to compute quark and gluon splitting functions in non-equilibrium QCD with arbitrary distribution functions, generalizing the Altarelli-Parisi equations.

Findings

Derived explicit expressions for non-equilibrium splitting functions.

Compared non-equilibrium splitting functions with vacuum results.

Provided a framework for studying hadronization in quark-gluon plasma.

Abstract

The $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions $f_q({\vec p})$ and $f_g({\vec p})$, we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in $\alpha_s$. We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.