Production of top quark pairs in association with a hard gluon to order

The production of top quark pairs accompanied by a hard gluon in $e^+e^-$ annihilation is studied including next-to-leading order corrections in the strong coupling. At leading order, the fraction r of $t\bar{t}g$ events with respect to all $t\bar{t}$ events is computed analytically as a function of the minimal gluon energy. Next-to-leading order results for r are given for center-of-mass energies of 0.5 and 1 TeV. We further calculate the differential distribution of r with respect to several variables, including the top quark energy and the $t\bar{t}$ invariant mass. We then investigate how our results depend on the choice of the renormalization scheme for the top quark mass by comparing results expressed in terms of either the pole mass or the $\overline{\rm MS}$ mass. Finally we estimate the sensitivity of the fraction r on the value of the running top quark mass at a scale of 1 TeV