  We detail a calculation of W gamma production in hadronic collision, at
Next-to-Leading Order (NLO) QCD interfaced to a shower generator according to
the POWHEG prescription supplemented with the MiNLO procedure. The fixed order
result is matched to an interleaved QCD+QED parton shower, in such a way that
the contribution arising from hadron fragmentation into photons is fully
modeled. In general, our calculation illustrates a new approach to the fully
exclusive simulation of prompt photon production processes accurate at the NLO
level in QCD. We compare our predictions to those of the NLO program MCFM,
which treats the fragmentation contribution in terms of photon fragmentation
functions. We also perform comparisons to available LHC data at 7 TeV, for
which we observe good agreement, and provide phenomenological results for
physics studies of the W gamma production process at the Run II of the LHC. The
new tool, which includes W leptonic decays and the contribution of anomalous
gauge couplings, allows a fully exclusive, hadron-level description of the W
gamma process, and is publicly available at the repository of the POWHEG BOX.
Our approach can be easily adapted to deal with other relevant isolated photon
production processes in hadronic collisions.
