Three-jet heavy b-quark production rates in $e^{+}e^{-}$ annihilations at the Z peak applied to test the flavour-independence of strong interactions using NLO QCD calculations

NLO theoretical calculations including mass effects allow performmg experimental tests of QCD. Precise determinations of the ratio abs/audssasb/asuds performed by DELPHI, SLD and OPAL collaborations have confirmed the flavour independence of the strong interactions. Two compatible values of the b-quark running mass, mb(Mz)mb(Mz) as defined in the MS scheme at the Mz scale have been extracted by DELPHI and SLD.