Next-to-Leading Order QCD Corrections to Three-Jet Cross Sections with Massive Quarks

We calculate the cross section for $e^{+}{e}^{-}$ annihilation into three jets for massive quarks at next-to-leading order in perturbative QCD, both on and off the $Z$ resonance. Our computation allows the implementation of any jet clustering algorithm. We give results for the three-jet cross section involving $b$ quarks for the JADE and Durham algorithms at c.m. energies $\sqrt{s}{=m}_Z$. We also discuss a three-jet observable that is sensitive to the mass of the $b$ quark.