Next-to-Leading Order QCD Corrections and Massive Quarks in $e^+e^-\to 3$ Jets

We present in detail a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate the soft and collinear divergencies of the four parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three jet configurations. We show next-to-leading order results for the three jet fraction, the differential two jet rate, and for the thrust distribution at various c.m. energies.