Le Higgs et le quark top dans le formalisme des relations de dispersion et le modèle standard

The mechanism of spontaneous symmetry breaking responsible for the generation of masses for both the bosons and the fermions of the Standard Model remains a mystery, especially that the Higgs has still not been discovered. In this thesis I concentrate on the study of the scalar sector of the Standard Model where the Higgs with the other Goldstone Boson reside. This sector can best be probed through the massive vector bosons and the top quark. The former, for their privileged coupling to the Higgs and because their longitudinal mode represents the Goldstone Bosons, and the top, because of its very strong Yukawa coupling, are very sensitive to the mechanism of symmetry breaking. I first focus on a situation where the Higgs is light and study the processes ${W^-W^+ \to t\bar{t}}$ and ${ZZ \to t\bar{t}}$. In order to unambiguously reveal a sign of New Physics, the Standard Model needs to be predicted precisely. In a first step I therefore study the electroweak and QCD one-loop corrections for these processes. This requires a renormalisation of the electroweak gauge and top sectors and mastering some one-loop techniques. I then concentrate on extracting the purely electroweak contributions to the above processes after setting up an analytical formula for the universal photonic contribution. The New Physics affecting the top and $W$ system is parameterised with the help of effective operators describing symmetry breaking. The effect of these operators is carefully compared to the effect of the one-loop radiative corrections before setting a limit on the parameters of these New Physics operators. To give more realistic results the $WW$ and $ZZ$ cross sections are turned into $e^+e^-$ and $pp$ cross sections by using a structure function approach. This allows an application to the phenomenology at futur colliders (LHC:Large Hadron Collider and ILC: International Linear Collider). A second aspect of the work presented here concerns the situation where the Higgs is heavy. For a heavy Higgs the electroweak interaction enters a strong interaction regime where perturbative unitarity may be violated, so we have to resort tonon-perturbative methods. By following the pioneering work of Contogouris, I construct a dispersive model for the process $W_LW_L \to W_LW_L$ where $W_L$ is the longitudinal $W$. The numerical resolution of the integral equation that is induced by this model enables a study of the strong effects of the electroweak interaction at high energies. I also extract a new limit for the validity of the perturbative calculation in the electroweak theory and a value for the Higgs mass in case the Higgs is very heavy.