Next-to-Leading-Order Predictions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>-Channel Single-Top Production at Hadron Colliders

Abstract

We present the predictions at next-to-leading order (NLO) in the strong coupling for the single-top cross section in the $t$ channel at the Tevatron and the LHC. Our calculation starts from the $2\ensuremath{\rightarrow}3$ Born amplitude $gq\ensuremath{\rightarrow}t\overline{b}{q}^{\ensuremath{'}}$, keeping the $b$-quark mass nonzero. A comparison is performed with a traditional NLO calculation of this channel based on the $2\ensuremath{\rightarrow}2$ Born process with a bottom quark in the initial state. In particular, the effect of using kinematic approximations and resumming logarithms of the form $\mathrm{log}({Q}^{2}/{m}_{b}^{2})$ in the $2\ensuremath{\rightarrow}2$ process is assessed. Our results show that the $2\ensuremath{\rightarrow}3$ calculation is very well behaved and in substantial agreement with the predictions based on the $2\ensuremath{\rightarrow}2$ process.