76 f(-p1) + f(-p2) W-(e-(p3) + ν(p4)) + Z(μ-(p5) + μ+(p6))

76.1 Di-boson production, processes 61–89

These processes represent the production of a diboson pair V 1V 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 1V 2 process at O(αs) 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. [23].

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 qT-slicing. They can be computed at NNLO using zero-jettiness slicing and qT-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 αs2. Two loop results for virtual diagrams at O(αs2) are taken from [5].

76.1.1 WZ production, processes 71–80

This process is calculable at LO,NLO and NNLO and has been treated in several papers, [2364]. For WZ production, the W is chosen to decay leptonically. The Z (or virtual photon, when appropriate) may decay into electrons (nproc=71,76), neutrinos (nproc=72,77), a pair of bottom quarks (nproc=73,78), three generations of down-type quarks (nproc=74,79) or two generations of up-type quarks (nproc=75,80). In process 78 the mass of the b-quark is neglected. These processes will be observed in the final state as W-boson + two or three jets. In processes 72 and 77, a sum is performed over all three species of neutrinos.

When removebr is true in processes 71 and 76, neither the W or the Z boson decays.

76.2 Anomalous Couplings

76.3 Input files for non-local subtraction, refs. [4]

76.4 Input files for transverse momentum resummation, ref. [7]

76.5 Input files for jet-vetoed cross-sections[8]

76.6 Plotter

nplotter_VV.f is the default plotting routine.

76.7 Example input and output file(s)

input76.ini process76.out

References

[1]    L.J. Dixon, Z. Kunszt and A. Signer, Helicity amplitudes for O(αs) production of W+W-, WZ, ZZ, Wγ, or 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 qqV 1V 2 4 leptons, JHEP 09 (2015) 128 [1503.04812].

[6]    R. Boughezal, J.M. Campbell, R.K. Ellis, C. Focke, W. Giele, X. Liu et al., Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77 (2017) 7 [1605.08011].

[7]    J.M. Campbell, R.K. Ellis, T. Neumann and S. Seth, Transverse momentum resummation at N3LL+NNLO for diboson processes, 2210.10724.

[8]    J.M. Campbell, R.K. Ellis, T. Neumann and S. Seth, Jet-veto resummation at N3LLp+NNLO in boson production processes, 2301.11768.