On the dependence of QCD splitting functions on the choice of the evolution variable

TL;DR

This paper investigates how the choice of evolution variable affects the NLO DGLAP splitting functions, providing explicit examples and identifying classes of variables that preserve the standard kernels.

Contribution

It demonstrates the dependence of NLO splitting functions on the evolution variable and identifies classes of variables that keep the kernels unchanged.

Findings

NLO Pqq kernel depends on the evolution variable.

Explicit example using maximum transverse momentum as the variable.

Identification of variable classes that preserve the standard kernel.

Abstract

We show that already at the NLO level the DGLAP evolution kernel Pqq starts to depend on the choice of the evolution variable. We give an explicit example of such a variable, namely the maximum of transverse momenta of emitted partons and we identify a class of evolution variables that leave the NLO Pqq kernel unchanged with respect to the known standard MS-bar results. The kernels are calculated using a modified Curci-Furmanski-Petronzio method which is based on a direct Feynman-graphs calculation.