Top-down and bottom-up excursions beyond the Standard Model: The example of left-right symmetries in supersymmetry

The field of high-energy physics has been living a very exciting period of its history with the Large Hadron Collider (LHC) at CERN collecting data. Indeed, this enormous machine able to collide protons at a center of mass energy of 14 TeV promises to unveil the mystery around the physics at such energy scales. From the physicists side, the expectations are very strong as it is nowadays a certitude that the Standard Model of particle physics is incomplete and should, in fact, be interpreted as the effective theory of a more fundamental one. Unfortunately, the 7 and 8 TeV runs of the LHC did not provide any sign of new physics yet but there has been at least one major discovery in 2010, namely the discovery of a scalar particle with a mass of 125 GeV and which properties are very close to those of the Standard Model Higgs boson. Since then, many questions have come up as we now want to understand if it really is the Standard Model Higgs boson or if it exhibits any deviations. It is in this peculiar context that my research work was carried. In a first project, we, my supervisors, our collaborator and I, have wanted to explore the phenomenology associated with the neutralinos and charginos sector of the left-right symmetric supersymmetric model. Such an analysis can be motivated by several reasons such as the fact that the supersymmetric nature of these models provides a natural explanation for the infamous hierarchy problem, implies the unification of the gauge coupling constants at very high energy and provides a natural candidate for dark matter. In addition to these nice features, the left-right symmetry introduces a natural framework for explaining the smallness of neutrino masses but also helps in addressing several other unresolved issues in the Standard Model framework. Only focusing on the lightest charginos and neutralinos decaying into one or more light leptons, we have shown in our study that these models can be easily discovered in multi-leptonic final states as they lead to signatures very different from those induced by the Standard Model or its supersymmetric version. In a second project, we have explored the phenomenology associated with doubly-charged particles. The discovery of such particles would be an irrefutable proof of new physics but would also raise the problem of knowing which model describes best their properties. Starting from the hypothesis that a particle carrying a two-unit electric charge is discovered at the LHC, we have carried an analysis which aim was to provide some key observables that would help in answering the latter question. To do so, we have adopted a model-independent approach where the Standard Model field content is extended minimally to contain a scalar, fermionic or vector multiplet transforming either as a singlet, doublet or triplet under SU(2)_L. The hypercharge of the latter field is chosen so that the highest electric charge carried by its components is equal to two and the Standard Model Lagrangian is extended to account for the new interactions. In our results, we have shown that the experimental constraints could be evaded easily so that the new fields can have a mass at least equal to 100 GeV. In addition, we have shown that, in the hypothesis that no other signal of new physics exists, only a combination of several kinematical distributions can help in distinguishing between the cases we have considered. Another part of my thesis, complementary to the phenomenology work, has consisted in developing computer programs that might be helpful for phenomenological studies. Working in the framework of the Mathematica package FeynRules, I took part in the development of a routine able to extract automatically the analytical expressions of the renormalization group equations at the two-loop level for any renormalizable supersymmetric model. I have also been involved in the development of another module of FeynRules able to extract automatically the analytical expressions for the mass matrices associated to any model implemented in FeynRules and to export these equations in the form of a C++ source code able to diagonalize the matrices and store the mixing matrices as well as the spectrum in an SLHA-compliant file. (author)