The strong coupling constant for b quarks has been determined, and its
flavour independence, as predicted by QCD, investigated. The analysis
involved events with lepton candidates selected from approximately 35
6 000 hadronic decays of the Z0, collected by the DELPHI detector at L
EP in 1990 and 199 1. A method based on a direct comparison of the thr
ee-jet fraction in a b enriched sample, selected by requiring leptons
with large momenta and transverse momenta, to that of the entire hadro
nic sample, illustrated the significant effect of the b quark mass on
the multi-jet cross section, and verified the flavour independence of
the strong coupling constant to an accuracy of +/- 6%. A second proced
ure based on a fit to the momentum and transverse momentum spectra of
the lepton candidates in both two-jet and three (or more)-jet event sa
mples simultaneously determined the b content in each, and, using seco
nd order QCD calculations, gave an absolute measurement of alpha(s) fo
r b quarks of 0. 1 18 +/- 0.004 (stat.) +/- 0.003 (syst.) +/- 0.008 (s
cale). A comparison with a, for all quark flavours, as measured from t
he three-jet fraction in all hadronic events, further allowed the coup
ling strength for b quarks to be expressed in terms relative to that f
or udsc quarks, thereby cancelling certain common systematic uncertain
ties, and yielded alpha(s)b/alpha(s)udsc = 1.00 +/- 0.04 (stat.) +/- 0
.03 (syst.).