To implement the full matrix element in a simulation is not trivial, and it is only for the s-channel Higgs in the VV VV scattering (fig. 2.14e), that a detailed description of the virtuality of the incoming vector bosons and the dependent width of the Higgs state is treated correctly in the PYTHIA simulation.
All VV VV processes can also be included in PYTHIA but in a somewhat simpler framework where it is possible to treat the cancellations between the different diagrams . Based on the simulation of in total 1 600 000 VV VV events with different treatment of the vector boson scattering the uncertainties in the total cross section will be discussed in section 8.8. The simulations were performed with a 100 GeV cut on the pT of the hard scattering to avoid the divergence at pT = 0 from the photon propagator in the VV VV scattering (fig. 2.14b).