  We perform an analytic calculation of the one-loop amplitude for the W-boson
mediated process 0 \to d u-bar Q Q-bar l-bar 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 \to W(\to e nu) b b-bar with massive b-quarks is included in
the program MCFM. A comparison is performed with previous published work.
