These processes represent the production of a diboson pair V _{1}V _{2}, where V _{1}
and V _{2} may be either a W or Z∕γ^{*}. All the processes in this section may
be calculated at NLO with the exception of nproc=69. There are various
possibilities for the subsequent decay of the bosons, as specified in the sections
below. Amplitudes for the V _{1}V _{2} process at O(α_{s}) are taken from ref. [1].
We also include singly resonant diagrams at NLO for all processes in the
case zerowidth = .false.. For more details on this calculation, please see
Refs. [2, 3].

For processes 62, 63, 64, 65, 74 and 75 the default behaviour is that the hadronic decay products of the bosons are clustered into jets using the supplied jet algorithm parameters, but no cut is applied on the number of jets. This behaviour can be altered by changing the value of the variable notag in the file src/User/setnotag.f.

Calculations of processes 61, 71, 76, 81 and 82 can be performed at NLO by
subtraction, zero-jettiness slicing and q_{T}-slicing. They can be computed at NNLO
using zero-jettiness slicing and q_{T}-slicing, as described in ’Non-local slicing
approaches for NNLO QCD in MCFM’,[4]. For processes 61, 81 and 86 the NNLO
corrections include glue-glue initiated box diagrams which first contribute at
order α_{s}^{2}. Two loop results for virtual diagrams at O(α_{s}^{2}) are taken from
[5].

For WW production, both W’s can decay leptonically (nproc=61) or one may decay
hadronically (nproc=62 for W^{-} and nproc=64 for W^{+}). Corresponding to processes
62,64, processes 63,65 implement radiation in decay from the hadronically decaying
W’s. Process 69 implements the matrix elements for the leptonic decay of both W’s
but where no polarization information is retained. It is included for the
sake of comparison with other calculations. Processes 62 and 64 may be
run at NLO with the option todk, including radiation in the decay of the
hadronically decaying W. Processes 63 and 65 give the effect of radiation in the
decay alone by taking the sum of the choices virt and real, or equivalently
tota.

Note that, in processes 62 and 64, the NLO corrections include radiation from the hadronic decays of the W.

When removebr is true in processes 61 and 69, the W bosons do not decay.

Process 61 can be calculated at NNLO. The NNLO calculations include
contributions from the process gg → WW that proceeds through quark loops. The
calculation of loops containing the third quark generation includes the effect of the
top quark mass (but m_{b} = 0), while the first two generations are considered massless.
For numerical stability, a small cut on the transverse momentum of the W bosons is
applied: p_{T}(W) > 0.05 GeV for loops containing massless (first or second generation)
quarks, p_{T}(W) > 2 GeV for (t,b) loops. This typically removes less than 0.1% of the
total cross section. The values of these cutoffs can be changed by editing
src/WW/gg_ww.f and recompiling.

nplotter_VV.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] J.M. Campbell and R.K. Ellis, An Update on vector boson pair production at hadron colliders, Phys. Rev. D 60 (1999) 113006 [hep-ph/9905386].

[3] J.M. Campbell, R.K. Ellis and C. Williams, Vector boson pair production at the LHC, JHEP 07 (2011) 018 [1105.0020].

[4] J.M. Campbell, R.K. Ellis and S. Seth, Non-local slicing approaches for NNLO QCD in MCFM, 2202.07738.

[5]
T. Gehrmann,
A. von
Manteuffel
and
L. Tancredi,
The
two-loop
helicity
amplitudes
for
qq^{′}→ V _{1}V _{2} → 4
leptons,
JHEP
09
(2015)
128
[1503.04812].