Abstract
Hadronic Z decay data taken with the ALEPH detector at LEP1 are used to measure the three-jet rate as well as moments of various event-shape variables. The ratios of the observables obtained from b-tagged events and from an inclusive sample are determined. The mass of the b quark is extracted from a fit to the measured ratios using a next-to-leading order prediction including mass effects. Taking the first moment of the $y_3$ distribution, which is the observable with the smallest hadronization corrections and systematic uncertainties, the result is \[m_b(M_{\mathrm Z}) = \left[3.27 \pm 0.22 (\mathrm{stat}) \pm 0.22 (\mathrm{exp}) \pm 0.38 (\mathrm{had}) \pm 0.16 (\mathrm{theo})\right] \;\gevcc\quad. \] The measured ratio is alternatively employed to test the flavour independence of the strong coupling constant for b and light quarks.
Highlights
The advent of next-to-leading order (NLO) calculations for e+e− annihilation into quark pairs, which take full account of quark mass effects [1, 2, 3, 4], has opened up the possibility for further investigations of QCD, such as measurements of the flavour independence of the strong coupling constant [5, 6, 7] or measurements of the running b-quark mass at the Z mass scale [5, 8]
In order to obtain the final values for Rbpdert, subtracted from the measured ratio the contributions from anomalous Rbplert, and the error due to the triangle diagrams are first finite Monte Carlo (MC) statistics for the evaluation of purities and detector and tagging corrections is added to the statistical error of the data
For the extraction of the b-quark mass it is required that the uncertainty on the measured ratio be at the 1% level, and that at the same time the size of the hadronization correction (Table 2) be smaller than the measured mass effect, given by the deviation of Rbpdert from unity
Summary
The advent of next-to-leading order (NLO) calculations for e+e− annihilation into quark pairs, which take full account of quark mass effects [1, 2, 3, 4], has opened up the possibility for further investigations of QCD, such as measurements of the flavour independence of the strong coupling constant [5, 6, 7] or measurements of the running b-quark mass at the Z mass scale [5, 8]. For a running b-quark mass of about 3 GeV/c2 a 3% deviation from unity is observed in this ratio [5] This is because the large b-quark mass suppresses gluon radiation in a similar way to the suppression of bremsstrahlung for muons compared to electrons. In this analysis a set of event-shape observables has been employed in addition to the three-jet rate in order to study the b-quark mass dependence of the measured ratios of the observables in b and uds initiated events.
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