Trilinear Gauge Boson Couplings and W-Pair Production.

Within the Standard Model, the vector bosons not only couple with fermions, but they can also couple to each other in certain combinations. The coupling of three gauge bosons is known as a trilinear gauge boson interaction [35,36]. These occur when two oppositely charged W bosons couple to a photon or ${\rm Z}^{0}$ boson, as shown in figure 3.1. These are the only two possible TGC interactions in the electroweak sector. Gluons may couple with each other in many combinations.

The coupling of four gauge bosons in the electroweak sector is also possible [37,38,39]. There are four possible combinations within the Standard Model. The coupling of Four W bosons $({\rm W}^{+}{\rm W}^{-}{\rm W}^{+}{\rm W}^{-})$, the coupling of two W bosons and two ${\rm Z}^{0}$ bosons $({\rm W}^{+}{\rm W}^{-}{\rm Z}^{0}{\rm Z}^{0})$, the coupling of two W bosons and two photons $({\rm W}^{+}{\rm W}^{-}\gamma\gamma)$, and the coupling of two W bosons a ${\rm Z}^{0}$ boson and a photon $({\rm W}^{+}{\rm W}^{-}{\rm Z}^{0}\gamma)$. Measurements of the quartic couplings have been made at OPAL [40].

Figure 3.1: The self coupling of three gauge bosons, known as the Trilinear Gauge Vertex.

This thesis is only concerned with the trilinear gauge coupling of the ${\rm Z}^{0}$ and $\gamma$ bosons to ${\rm W}^{\pm}$ bosons. In this chapter the theoretical description of the trilinear gauge coupling will be discussed. It will then be shown that the main processes at LEP containing this coupling are W-pair production processes. Accordingly all possible W-pair production processes are then discussed. This will include the identification of the role that the spin of the W bosons take in this process and the Spin Density Matrix (SDM) will be introduced. Throughout, some theoretical predictions on what observations could be made through Standard Model and non-Standard Model interactions are given.