Scattering amplitudes in the five-dimensional gauge

This thesis investigates the behavior of scattering amplitudes in the electroweak sector of the Standard Model, with a particular focus on the energy dependence of individual Feynman diagrams in different gauges. Special attention is given to cases that appear to violate simple unitarity constraints, such as amplitudes involving longitudinally polarized weak bosons: certain diagrams exhibit energy growth, necessitating non-trivial cancellations among them to ensure the restoration of unitarity. It is therefore of interest to explore calculational methods that inherently implement these cancellations, preventing the appearance of spurious energy-growing terms. This work is specifically dedicated to studying an alternative approach in which the electroweak Lagrangian is expressed in a physical gauge. For simplicity we consider the limit where only the \( SU(2)_L \) symmetry remains active, corresponding to the vanishing weak mixing angle (\(\theta_W \to 0\)), yet the approach can be easily generalised to the Standard Model case. Additionally, the Higgs sector is formulated using the Higgs-Kibble model. This approach, inspired by the so-called ``Equivalent Gauge'', is promising as it introduces polarization vectors for longitudinal weak bosons that are independent of energy. A crucial first step in this programme is the analytical investigation of the Lagrangian structure, which can be rewritten in terms of five-dimensional fields \( w^\mu_a = (w^\mu_a, \phi_a) \), where \( w^\mu_a \) and \( \phi_a \) denote the gauge fields and their associated Goldstone bosons, respectively. After deriving the corresponding Feynman rules, I demonstrate that not only decay and scattering processes yield results consistent with those obtained in the unitary gauge, thereby confirming the validity of the method, but also that the energy behaviour of single diagrams is improved.