Phenomenology of flavour violation in supersymmetric models

Despite the lack of experimental evidence, Supersymmetry remains an attractive candidate for physics beyond the standard model of particle physics. Simple and viable supersymmetric extensions, such as the Minimal Supersymmetric Standard Model, cure, among other shortcomings of the standard model, the electroweak hierarchy problem, the gauge coupling unification and provide attractive dark matter candidates.One of the general characteristics of such extensions is that they may present a non-trivial flavour structure, which can lead to sizable contributions to flavour violating processes which are precisely measured and can be used to constrain the parameter space of new physics. The purpose of this manuscript is to discuss aspects of the extended flavour structure within supersymmetric models.The manuscript will first introduce the Standard Model of particle physics and its supersymmetric extensions before exposing three research projects.The first one will treat the problematic of the reconstruction of the squark flavour structure. Here, we have employed different strategies relying on inference statistical methods together with machine learning algorithms and assuming that a squark-like state is to be observed at colliders. Being a first step in this direction, improvement and complementary study will need to be proposed in case of the actual observation of a squark-like state but the obtained results are appealing.As a second step, we shall discuss constraints and experimental signatures of SU(5) Grand Unified Theories including flavour symmetries. In this framework, we will focus on A4 family symmetry inspired models. This analysis is based on a numerical scan of the parameter space, including experimental flavour constraints as well as dark matter relic density. The results show, as it has already been pointed out before, that the lepton sector is much more constraining that the hadronic one. Additionally, interesting features arise in case of a simultaneous scan over the flavour violating parameters, and suggest that the allowed ranges for these parameters are larger than in the case of a single parameter study because of correlation effects.Finally, the last chapter will be dedicated to leptoquark extensions of the standard model. These models, not necessary supersymmetric, have received considerable attention over the past few years, mainly due to the potential observation of lepton non universality at the Large Hadron Collider. We will discuss such extensions in the context of discrete flavour symmetries, useful tool for constraining the leptoquark patterns to a very predictive form. Finally, a model independent scan will be exposed, where we have obtained a list of potential symmetry candidates able to reproduce very specific leptoquark patterns alongside to the standard model fermionic mixing