m(b) at M-Z

The value of the Lr quark, mass at the M-Z scale defined in the <(MS)over bar> renormalization scheme, m(b)(M-Z), was determined using 2.8 million hadronic Z decays collected during 1992-1994 by the DELPHI detector to be m(b)(M-Z) = 2.67 +/- 0.25 (stat.) +/- 0.34 (frag.) +/- 0.27 (theo.) GeV/c(2). The analysis considers NLO corrections to the three-jet production rate including mass effects, and the result obtained agrees with the QCD prediction of having a running b quark mass at an energy scale equal to M-Z. This is the first time that such a measurement is performed far above the <b(b)over bar> production threshold. The study also verifies the flavour independence of the strong coupling constant for b and light quarks within 1% accuracy. (C) 1998 Elsevier Science B.V.