Minimal U(1) two-Higgs-doublet models for quark and lepton flavour

The Standard Model (SM) of particle physics describes numerous phenomena related to the interactions among the fundamental constituents of matter with remarkable precision. However, the observations of neutrino oscillations imply the existence of massive neutrinos and lepton mixing, which must be accounted through extensions of the SM. Additionally, the SM lacks a guiding principle to explain the observed fermion masses and their mixing -- this is often referred to as the flavour puzzle.

In this thesis, we address the flavour puzzle within the 2HDM, supplemented by horizontal Abelian symmetries and neutrino mass generation through effective Weinberg operators. To this end, we conduct a systematic analysis to determine the minimal quark and lepton flavour patterns imposed by these symmetries, compatible with the observed fermion masses, mixing, and CP violation phases. We determine four minimal models for quarks, where the number of independent parameters matches the number of observables.

For the lepton sector, three minimal predictive models are identified. Namely, we find scenarios with a preference for the upper/lower octant of the atmospheric mixing angle, that exhibit lower bounds on the lightest neutrino masses currently probed by cosmology and testable at future neutrinoless double beta decay experiments, even for a normally-ordered neutrino masses. We investigate the phenomenology of each model taking into account all relevant theoretical, electroweak precision observables, scalar sector constraints, as well as stringent quark flavour processes such as , and meson oscillations, and the charged lepton flavour-violating decays and . We show that, in some cases, Abelian flavour symmetries provide a natural framework to suppress flavour-changing neutral couplings and lead to scenarios featuring heavy neutral/charged scalar masses below the TeV scale within the reach of current experiments.