$m_b(m_Z)$ from jet production at the $Z$ peak in the Cambridge algorithm

We consider the production of heavy quark jets at the $Z$-pole at the next-to-leading order (NLO) using the {\it Cambridge jet-algorithm}. We study the effects of the quark mass in two- and three-jet observables and the uncertainty due to unknown higher order corrections as well as due to fragmentation. We found that the three-jet observable has remarkably small NLO corrections, which are stable with respect to the change of the renormalization scale, when expressed in terms of the {\it running quark mass} at the $m_Z$-scale. The size of the hadronization uncertainty for this observable remains reasonably small and is very stable with respect to changes in the jet resolution parameter $y_c$.