QCD corrections to the hadronic production of a heavy quark pair and a <em>W</em>-boson including decay correlations

We perform an analytic calculation of the one-loop amplitude for the $W$-boson mediated process 0 → $d\overline{u}Q\overline{Q}\overline{ℓ}ℓ$ retaining the mass for the quark $Q$. The momentum of each of the massive quarks is expressed as the sum of two massless momenta and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron + hadron → $W$(→ $eν$)$b\overline{b}$ with massive $b$-quarks is included in the program MCFM. A comparison is performed with previous published work.