  We present a detailed computation of the fully exclusive cross section of p +
antip --> W + photon + X with X = 0 and 1 jet in the framework of the
factorization theorem and dimensional regularization. Order alpha-strong and
photon bremsstrahlung contributions are discussed in the MS-bar mass
factorization scheme. The resulting expressions are ready to be implemented
numerically using Monte Carlo techniques to compute single and double
differential cross sections and correlations between outgoing pairs of
particles.
