0 v 1 2 0 A ug 1 99 7 Experimental determination of m b ( M Z ) in DELPHI

The quark masses are fundamental parameters of the QCD lagrangian which are not predicted by the theory. Their definition is not unique since quarks are not observed as free particles, but confined inside hadrons. Therefore, the use of dynamical expressions is mandatory in order to determine the masses of the quarks. The perturbative pole mass, Mq, and the running mass in the MS scheme, mq, are two definitions among the most frequently used. In the renormalization procedure of QCD, once the divergent part is subtracted, we deal with finite quantities for the strong coupling constant, αs, and the quark masses, mq. However, these quantities are not fixed parameters, but their actual value depends on the energy scale of the process being considered. In other words, αs and mb exhibit a running property. The running of αs has been verified many times by different experiments (for a review see [ 1, 2]). Although the running of the quark masses is as basic to QCD as that of αs, it has never been experimentally tested before. The empirical determination of the quark masses at different scales must be regarded as a fundamental test of QCD. Nowadays, the LEP I data allow measuring the b quark mass at the MZ scale (far away from the bb̄ production threshold), thus testing its running. According to the mb evolution, dictated by the Renormalization Group Equation (RGE), a change on mb of ∼ 1.3 GeV is expected when varying the scale from MΥ/2 up to MZ , as mb(MΥ/2) ≈ 4.16± 0.18 GeV/c 2 [ 3]. In ee →hadrons, the three-jet rate is an observable sensitive to the b mass. When testing the universality of αs by using the three-jet rate, it was observed that due to the mass effects, b quarks radiate a 3 to 5% less gluons than light quarks do [ 4]. So, reversing the argument: assuming the αs universality allows measuring the b quark mass by studying the three-jet rate. The former Leading Order (LO) calculations of the three-jet cross section in ee including mass terms [ 5, 6] are not appropriate in order to evaluate the b quark mass, as these calculations can not discern between Mb and mb. Recently, Next to Leading Order (NLO) expressions for the three-jet rate in ee are available [ 7, 8, 9], thus, enabling the measurement of mb. The observable used in this work is: