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

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 $\geq3$-jet fractions in $e^+e^-\to b\bar{b}$ vs. $e^+e^-\to q_l\bar{q_l}$ ($q_l$ = 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 $m_b(M_Z) = 2.56 \pm 0.27 (stat.) ^{+0.28}_{-0.38} (syst.) ^{+0.49}_{-1.48} (theor.) GeV/c^2$.