These processes represent the production of a W boson which subsequently decays
leptonically, in association with a real photon. Since this process includes a real
photon, the cross section diverges when the photon is very soft or in the direction of
the beam. Thus in order to produce sensible results, the input file must supply values
for both gammptmin and gammrapmax. Moreover, when the parameters zerowidth and
removebr are set to .false. the decay W → ℓν will include photon radiation from
the lepton, so that a non-zero R(γ,ℓ)_{min} (Rgalmin) should also be supplied. This will
ensure that the cross section is well-defined. Virtual amplitudes are taken from
ref. [1].

The calculation of processes 290 and 295 may be performed at NLO and NNLO using the Frixione algorithm [2] or standard isolation. Thec phenomenology of these processes at NNLO has been treated in ref. [3].

For processes 290 and 295 the role of mtrans34cut changes to become a cut on
the transverse mass on the M_{345} system, i.e. the photon is included with the leptons
in the cut.

Processes 292 and 297 represent the Wγ+jet production processes. They may be computed to NLO.

Processes 294 and 299 represent the photon-induced reactions, p + γ → eνγj and should be computed at NLO. Processes 2941 and 2991 represent the photon-induced reactions, p + γ → eνγjj and should be computed at NLO.

Processes 290-297 may also be computed including the effect of anomalous WWγ couplings, making use of the amplitudes calculated in Ref. [4]. Including only dimension 6 operators or less and demanding gauge, C and CP invariance gives the general form of the anomalous vertex [4],

| (2) |

where ŝ is the Wγ pair invariant mass.

The Standard Model cross section is obtained by setting Δκ^{γ} = λ^{γ} = 0.

nplotter_Vgamma.f is the default plotting routine.

[1]
L.J. Dixon,
Z. Kunszt
and
A. Signer,
Helicity
amplitudes
for
O(α_{s})
production
of
W^{+}W^{-},
W^{±}Z,
ZZ,
W^{±}γ,
or
Zγ
pairs
at
hadron
colliders,
Nucl.
Phys.
B531
(1998)
3
[hep-ph/9803250].

[2] S. Frixione, Isolated photons in perturbative QCD, Phys. Lett. B429 (1998) 369 [hep-ph/9801442].

[3] J.M. Campbell, G. De Laurentis, R.K. Ellis and S. Seth, The pp → W(→ lν) + γ process at next-to-next-to-leading order, JHEP 07 (2021) 079 [2105.00954].

[4] D. De Florian and A. Signer, W gamma and Z gamma production at hadron colliders, Eur. Phys. J. C16 (2000) 105 [hep-ph/0002138].