SUSY, Casimir scaling, and probabilistic properties of gluon and quark-jet evolution

We study the new relation [B. A. Kniehl and A. V. Kotikov, arXiv:1702.03193.] between the anomalous dimensions, resummed through next-to-next-to-leading logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments Dq,g(μ2) of the fragmentation functions, which correspond to the average multiplicities of hadrons in jets initiated by quarks and gluons, respectively. This relation is shown to lead to probabilistic properties of the properly rescaled parton jet multiplicities obtained from standard ones by extracting the quark and gluon "color charges" CF and CA, respectively.