THE REACTION e + e − → t¯tg AT NEXT-TO-LEADING ORDER IN αs ∗

The production of top quark pairs together with a hard gluon in e + e − annihilation is studied including next-to-leading order corrections in the strong coupling. 1 Motivation The production of top quark pairs in association with (at least) one additional parton X carrying a hard momentum k X , e + (p +) + e − (p −) → t(k t) + ¯ t(k¯ t) + X(k X), (1) is interesting for several reasons: A comparison of the cross section for (1) (which will be properly defined below) to the inclusive t ¯ t production cross section allows a measurement of the strong coupling constant α s. A deviation of this measurement from the determination of α s using event samples containing light quark jets would indicate a violation of the " flavour independence " of the strong interactions — i.e., would point towards new physics phenomena connected with the top quark. Specific examples of non-standard interactions that could be probed by reaction (1) are possible anomalous couplings of the top quark to photons, Z-bosons and gluons. It has been shown 1 that a large anomalous chromomagnetic t ¯ tg coupling would modify the gluon energy spectrum in e + e − → t ¯ tg. Furthermore, symmetry tests can be performed utilizing the richer kinematic structure of the final state in (1). These contain tests of the CP symmetry 2 and the search for final state rescattering ('T'-violating) effects using triple momentum correlations. 3 Both the search for heavy quark anomalous couplings 4 and the symmetry tests 5 have been shown to be experimentally feasible in the case of b ¯ bg production at the Z resonance, and it will be interesting to perform similar studies with top quarks. In order to unravel possible deviations from QCD expectations, it is mandatory to analyse reaction (1) at next-to-leading order in α s. 2 Leading order analysis At order α s , the additional parton X in (1) can only be a gluon. The cross section for e + e − → t ¯ tg develops a soft singularity as the gluon energy goes to zero. An infrared finite cross section can be defined by demanding x g ≡ 2E g / √ s > x cut , where E g is the gluon energy in the c.m. system, √ s is the c.m. energy, and x cut is …