SUSY-like relation in evolution of gluon and quark jet multiplicities

TL;DR

This paper derives a new, exact relationship between quark and gluon jet multiplicities in QCD, improving previous models by enabling precise solutions of evolution equations without relying on supersymmetry.

Contribution

It introduces a supersymmetry-like relation in the DGLAP evolution equations for jet multiplicities, independent of quark flavors, allowing for exact solutions.

Findings

Derived a new relation between quark and gluon anomalous dimensions.

Achieved an exact solution to the evolution equations for jet multiplicities.

Enhanced understanding of jet multiplicity evolution in QCD.

Abstract

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments D{q,g}(\mu2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship, which is independent of the number of quark flavors, strongly improves previous treatments by allowing for an exact solution of the evolution equations. So far, such relationships have only been known from supersymmetric QCD.