Next-to-Leading-Order Predictions fort-Channel Single-Top Production at Hadron Colliders

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 $2\to 3$ Born amplitude $gq\to t\overline{b}{q}^{\prime }$, keeping the $b$-quark mass nonzero. A comparison is performed with a traditional NLO calculation of this channel based on the $2\to 2$ Born process with a bottom quark in the initial state. In particular, the effect of using kinematic approximations and resumming logarithms of the form $\log (Q^2/m_b^2)$ in the $2\to 2$ process is assessed. Our results show that the $2\to 3$ calculation is very well behaved and in substantial agreement with the predictions based on the $2\to 2$ process.