Determination of the QCD color factor ratio C{sub A}/C{sub F} from the scale dependence of multiplicity in three jet events

I examine the determination of the QCD color factor ratio C{sub A}/C{sub F} from the scale evolution of particle multiplicity in e{sup +}e{sup -} three jet events. I fit an analytic expression for the multiplicity in three jet events to event samples generated with QCD multihadronic event generators. I demonstrate that a one parameter fit of C{sub A}/C{sub F} yields the expected result C{sub A}/C{sub F}=2.25 in the limit of asymptotically large energies if energy conservation is included in the calculation. In contrast, a two parameter fit of C{sub A}/C{sub F} and a constant offset to the gluon jet multiplicity, proposed in a recent study, does not yield C{sub A}/C{sub F}=2.25 in this limit. I apply the one parameter fit method to recently published data of the DELPHI experiment at the e{sup +}e{sup -} collider LEP at CERN and determine the effective value of C{sub A}/C{sub F} from this technique, at the finite energy of the Z{sup 0} boson, to be 1.74{+-}0.03{+-}0.10, where the first uncertainty is statistical and the second is systematic. (c) 2000 The American Physical Society.