Measurement of the running b-quark mass using $e^{+}{e}^{-}\to b\bar{b}g$ events

Abstract

We have studied the determination of the running b-quark mass, $m_b(M_Z)$, using $Z^0$ decays into 3 or more hadronic jets. We calculated the ratio of $\ge 3$-jet fractions in $e^{+}{e}^{-}\to b\bar{b}$ vs. $e^{+}{e}^{-}\to q_l\overline{q_l}$ ($q_l$ = u or d or s) events at next-to-leading order in perturbative QCD using six different infra-red- and collinear-safe jet-finding algorithms. We compared with corresponding measurements from the SLD Collaboration and found a significant algorithm-dependence of the fitted $m_b(M_Z)$ value. Our best estimate, taking correlations into account, is $m_b(M_Z)=2.56\pm 0.27(stat.{)}_{-0.38}^{+0.28}(syst.{)}_{-1.48}^{+0.49}(theor.)GeV/c^2$.

22 pages (LaTeX), 1 Postscript figure. Version to appear in Phys. Lett. B. Several clarifying remarks added in the text, typos corrected, and theoretical results for very small masses added in the figure

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