Measurement of the running b-quark Mass using e{sup +}e{sup -} {yields} b{bar b}g events

We have studied the determination of the running b-quark mass, m{sub b}(M{sub Z}), using Z{sup 0} decays into 3 or more hadronic jets. We calculated the ratio of {ge} 3-jet fractions in e{sup +}e{sup -} {yields} b{bar b} vs. e{sup +}e{sup -} {yields} q{sub l}{bar q}{sub l} (q{sub l} = u or d or s) events at next-to-leading order in perturbative QCD using six different infra-red- and collinear-safe jet-finding algorithms. We compared with corresponding measurements from the SLD Collaboration and found a significant algorithm-dependence of the fitted m{sub b}(M{sub Z}) value. Our best estimate, taking correlations into account, is m{sub b}(M{sub Z}) = 2.52 {+-} 0.27(stat.){sub -0.47}{sup +0.33}(syst.){sub -1.46}{sup +0.54}(theor.) GeV/c{sup 2}