Determination of the b quark mass at the Z mass scale

In hadronic decays of Z bosons recorded with the OPAL detector at LEP, events containing b quarkswere selected using the long lifetime of b flavoured hadrons. Comparing the 3-jet rate in b events with that in d,u,s and c quarkevents, a significant difference was observed. Using \({\cal O}(\alpha_{\mathrm{S}}^2)\) calculations for massive quarks, this difference was used to determine the b quarkmass in the \({\ overline{\mathrm{{MS}}}}\) renormalisation scheme at the scale of the Z boson mass. By combining the results from seven different jet finders the running b quarkmass was determined to be \({\ overline{m}_{b}}({m_{Z}}) = (2.67 \pm 0.03{\mathrm{(stat.)}} ^{+0.29}_{-0.37}{\mathrm{(syst.)}} \pm 0.19{\mathrm{(theo.)}}){\mathrm{ GeV}}\). Evolving this value to the b quarkmass scale itself yields \({\ overline{m}_{b}}({\ overline{m}_{b}}) = (3.95 ^{+0.52}_{-0.62}){\mathrm{ GeV}}\), consistent with results obtained at the b quarkproduction threshold. This determination confirms the QCD expectation of a scale dependent quarkmass. A constant mass is ruled out by 3.9 standard deviations.