Study of the Electroweak Symmetry Breaking Sector for the LHC

Abstract

In this dissertation, a strongly interacting Electroweak Symmetry Breaking Sector is considered. The framework of Effective Field Theories (EFT) and unitarization procedures is used here. Such a framework successfully explained the appearance of resonances in low energy QCD some decades ago. The EFT are computed at the Next to Leading order (NLO). If new resonances were discovered at the LHC run-II, different theoretical approaches could be used to study them. However, the framework that we follow here has several advantages. For instance, it only contains a few parameters. Seven in the case of scattering inside the Electroweak Symmetry Breaking Sector (WL WL, ZL ZL and hh). A few more if the gamma-gamma and tt states are included. And, even more important, the masses and widths of the resonances emerge as a consequence of the low-energy behaviour of the theory. They are not free parameters of the model, it is sufficient with those from the Lagrangian. The EFTs for longitudinal gauge bosons plus Higgs are being actively investigated, because of their direct application to the experimental program of the LHC run-II. However, they are frequently considered only as a useful parameterization of slight deviations from the Standard Model behaviour. In other cases, they are extended to implement new resonances in an explicit way. Our approach shares with these models the use of an EFT in the very first steps, as well as the experimental bounds over the parameters of the Effective Lagrangian. If we use only EFT, the perturbative expansion breaks down because it is derivative. In our work below, EFT can be efficiently extended to cover the regime of saturation of unitarity. This is achieved by dispersion relations, whose subtraction constants and left cut contribution can be approximately obtained in different ways giving rise to different unitarization procedures. Several unitarization procedures have been considered. We have studied in deeper detail three of them, since they have the best properties. The chosen methods are the Inverse Amplitude Method, one version of the N/D method and another improved version of the K-matrix. A modified version of the first two ones is used for the coupling with gamma-gamma and tt. In all the cases we get partial waves which are unitary, analytical with the proper left and right cuts and in some cases poles in the second Riemann sheet that can be understood as dynamically generated resonances. A new numerical method has been developed in order to look for such poles. We also point out that the unitarization formalisms are also extended to the coupled channel. This is a novelty, and implies the possibility that an hypothetical resonance comes from a strongly process like VV to hh to VV (V stands for a longitudinal gauge boson). Such a resonance would be triggered by the coupling VVhh (parameter b of the EFT), which is less constrained that the coupling VVh (parameter a). Finally, all this work is given in a form that it could be implemented in a Monte Carlo (MC) simulation program, in order to generate MC events for the LHC Run-II or future collider experiments.