  An experimental study of the normalized three-jet rate of b quark events with
respect to light quarks events (light= \ell \equiv u,d,s) has been performed
using the CAMBRIDGE and DURHAM jet algorithms. The data used were collected by
the DELPHI experiment at LEP on the Z peak from 1994 to 2000. The results are
found to agree with theoretical predictions treating mass corrections at
next-to-leading order. Measurements of the b quark mass have also been
performed for both the b pole mass: M_b and the b running mass: m_b(M_Z). Data
are found to be better described when using the running mass. The measurement
yields: m_b(M_Z) = 2.85 +/- 0.18 (stat) +/- 0.13 (exp) +/- 0.19 (had) +/- 0.12
(theo) GeV/c^2 for the CAMBRIDGE algorithm. This result is the most precise
measurement of the b mass derived from a high energy process. When compared to
other b mass determinations by experiments at lower energy scales, this value
agrees with the prediction of Quantum Chromodynamics for the energy evolution
of the running mass. The mass measurement is equivalent to a test of the
flavour independence of the strong coupling constant with an accuracy of 7
permil.
