mb at MZ

The value of the b quark mass at the M Z scale defined in the MS 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 production threshold. The study also verifies the flavour independence of the strong coupling constant for b and light quarks within 1% accuracy.