V_LV_L background

 The production of final states with longitudinal polarised vector bosons can to the lowest order be described accurately by the effective W approximation (section 2.2.2) using the diagrams from fig. 2.14 for the vector boson interaction. There are interference effects between the different diagrams and some of the individual diagrams diverge for large centre of mass energies, $\sqrt{\hat{s}}$ , in the hard scattering. For this reason it is not possible to distinguish the different processes and in fact the sum of all should be regarded as the signal of a heavy Higgs particle.

To implement the full matrix element in a simulation is not trivial, and it is only for the s-channel Higgs in the VV $\rightarrow$ VV scattering (fig. 2.14e), that a detailed description of the virtuality of the incoming vector bosons and the $\hat{s}$ dependent width of the Higgs state is treated correctly in the PYTHIA simulation.

All VV $\rightarrow$ 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 [74]. Based on the simulation of in total 1 600 000 VV $\rightarrow$ 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 p_T of the hard scattering to avoid the divergence at p_T = 0 from the photon propagator in the VV $\rightarrow$ VV scattering (fig. 2.14b).