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We show the new relationship [1] between the anomalous dimensions, resummedthrough next-to-next-to-leading-logarithmic order, in theDokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for thefirst Mellin moments D{q,g}(\mu2) of the quark and gluon fragmentationfunctions, which correspond to the average hadron multiplicities in jetsinitiated by quarks and gluons, respectively. This relationship, which isindependent of the number of quark flavors, strongly improves previoustreatments by allowing for an exact solution of the evolution equations. Sofar, such relationships have only been known from supersymmetric QCD.

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