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 algorithm at c.m. energies √ s = m Z . We also discuss a three-jet observable that is sensitive to the mass of the b quark. PACS number(s): 12.38. Bx, 13.87.Ce, 14.65.Fy Typeset using REVT E X * supported by BMBF, contract 057AC9EP(1). † supported by Deutsche Forschungsgemeinschaft.
1Jets of hadrons, which originate from the production and subsequent fragmentation of quarks and gluons in high energy electron positron annihilation have been among the key predictions [1,2] of quantum chromodynamics (QCD). For precision tests of QCD the e + e − experiments provide a particularily clean set-up. There exist a number of jet observables that are well-defined (i.e., infrared-finite) in QCD, and which can be calculated perturbatively as an expansion in the strong coupling α s . The next-to-leading order (NLO) QCD corrections to three-jet production were computed more than a decade ago [3,4] for massless quarks, and subsequent implementations [5-9] of these results have been widely used for tests of QCD with jet physics.To date huge samples of jet events produced at the Z resonance have been collected both at LEP and SLC. From these data large numbers of jet events involving b quarks can be isolated with high purity using vertex detectors. For detailed investigations of b jets quark mass effects must be taken into account in the theoretical predictions [10]. Specifically, knowledge of the NLO three-jet fraction for non-zero quark mass opens the possibility to measure the mass of the b quark from b jet data at the Z peak [11]. Further applications include precision tests of the asymptotic freedom property of QCD by means of three-jet rates measured at various center-of-mass energies, also far below the Z resonance [12].As far as massive quarks are concerned the three, four, and five jet rates are known to leading order (LO) in α s only [13][14][15]. In this Letter we report the calculation of the e + e − annihilation cross section into three jets involving a massive quark antiquark pair at next-to-leading order QCD [16,17]. The determination of this cross section σ 3 N LO to order α 2 s consists of two parts: First, the computation of the amplitude of the partonic reaction e + e − → γ * , Z * → QQg at leading and next-to-leading order in the QCD coupling. Here Q denotes a massive quark and g a gluon. We have calculated the complete decay amplitude and decay distribution structure for this reaction. This allows for predictions including oriented three-jet events. The differential cross section involves the so-called hadronic tensor 2 which contains five parity-conserving and four parity-violating Lorentz structures. Second, the leading order matrix elements of the four-parton product...