Improvement measurements of the b quark mass at LEP

An improved determination of the b-quark mass at the Mz scale, mb(Mz), has been obtained by the DELPHI and OPAL experiments at LEP. The normalized three-jet rate of b-quarks with respect to light quarks, R3bl, has been measured with different jet clustering algorithms and compared with the massive NLO calculations to extract mb(Mz). For DELPHI, the increase in statistics and a better understanding of the flavour tagging, hadronization process and the gluon splitting rates leads to a precision of 380 MeV. The effect of the b-quark mass on the four-jet rate has also been studied by DELPHI