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 i n 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 correspo nding theoretical expression provides a good description of available gluon jet measurements. In contrast, the 3NLO correction to the quark jet multip licity is large and the theoretical expression does not describe the data a ccurately. It is shown that the well known success of the next-to-leading o rder (NLO) approximation in describing the energy evolution of quark jet mu ltiplicity can be attributed to the equivalence of the quark and gluon expr essions at NLO to within a constant factor, and to almost constant contribu tions from higher order terms to the gluon jet result. (C) 1999 Published b y Elsevier Science B.V. All rights reserved.