EXCALIBUR

EXCALIBUR [75] is the most widely used generator. It contains not only the Standard Model matrix elements, but also the option to switch on a number of the anomalous couplings seen in the general Lagrangian, equation 3.1. The couplings that can be varied are; $g^{z}_{1}$, $\kappa_{\gamma}$, $\kappa_{z}$, $\lambda_{\gamma}$, $\lambda_{z}$, and $g^{z}_{5}$. They may be set at any value. It is not possible to implement the CP-violating couplings.

EXCALIBUR generates four-fermion final states through all possible electroweak four-fermion processes [74]. However, the QED two-photon diagram is omitted from the OPAL version because this process is not well understood and is better modelled by dedicated two-photon generators. This means that the interference terms of this process with the other NC48 diagrams are neglected. This is thought to be a small effect, especially compared to the uncertainty associated with the two-photon process itself.

Figure 5.5: The interfering QCD background.

All fermions are assumed to be massless when they are generated. The generator also includes the width of the ${\rm W}^{\pm}$ and ${\rm Z}^{0}$ bosons. QED initial state corrections are implemented using a structure function formalism [76]. Interfering QCD backgrounds [77] are also possible. An example of these diagrams are as in figure 5.5. These interfering backgrounds are only relevant for the ${\rm q\bar{\rm q}q\bar{\rm q}}$ channel and in the OPAL version of EXCALIBUR they are not implemented. This is to avoid double-counting because they are also contained in the standard PYTHIA quark pair production Monte Carlo that is used as the background generator for the ${\rm q\bar{\rm q}q\bar{\rm q}}$ channel. EXCALIBUR has a Coulomb correction [78] for the CC03 WW production. This correction accounts for the fact that if the two W bosons are travelling slowly with respect to each other, the pure Coulomb attraction between them is not negligible, and it changes the W boson momentum distribution. This effect is particularly important at the W-pair production threshold of 161 GeV.

A naive QCD correction is also implemented in EXCALIBUR. This is because, in addition to the four-fermion production that EXCALIBUR models, there is also four-fermion plus one-gluon production which enhances the WW production cross-section. The correction is applied naively to all final-states with W $\rightarrow$q $\bar{\rm q}$ decays and it boosts the cross-section by $(1+\alpha_{s}($$\mbox{${\rm M}_{\rm W}$}$$)/\pi)$ for each W $\rightarrow$q $\bar{\rm q}$ decay. It should be noted that the W $\rightarrow$q $\bar{\rm q}$g topology is simulated in the events by the parton-shower part of the event generation, so multiplying the cross-section by this correction is a reasonable thing to do.

The naive QCD correction in principle should be applied to all diagrams with a vector boson V $\rightarrow$q $\bar{\rm q}$ decay. However to achieve this $\alpha_{s}$(Q$^2$) has to be evaluated at the correct (vector boson mass) scale Q$^{2}$. This is extremely involved, so the naive QCD correction is only applied to the WW diagrams, where Q is well defined ( ${\rm M}_{\rm W}$).