Energy dependence of mean multiplicities in gluon and quark jets at the next-to-next-to-next-to-leading order

Analytic predictions for the energy dependence of the mean multiplicities in gluon and quark jets are presented at the next-to-next-to-next-to-leading order (3NLO) of perturbative QCD and are compared to experiment. The 3NLO correction to the gluon jet multiplicity is found to be small. The corresponding theoretical expression provides a good description of available gluon jet measurements. In contrast, the 3NLO correction to the quark jet multiplicity is large and the theoretical expression does not describe the data accurately. It is shown that the well known success of the next-to-leading order (NLO) approximation in describing the energy evolution of quark jet multiplicity can be attributed to the equivalence of the quark and gluon expressions at NLO to within a constant factor, and to almost constant contributions from higher order terms to the gluon jet result.