Lepton flavour non-universality. From effective field theory to extended gauge models

The experimental averages of the ratios R(D${}^{\left(\text{â}\text{ˆ}\text{—}\right)}$), testing lepton flavour universality in the decays B→D${}^{\left(\text{â}\text{ˆ}\text{—}\right)}\ell$ν, exceed the Standard Model prediction by 1.4σ and 2.5σ respectively. Taking correlations into account, these tensions result in a combined difference above 3.1σ. This thesis focuses on analysing possible scenarios of Physics beyond the Standard Model to solve this tension, following a bottom-up approach: the first part is focused on a global analysis of the b→cτν data, including the newly released polarisation observables, in terms of an effective field theory, considering scenarios with a single additional particle mediating the decay. This analysis allows us to infer which virtual particle is more likely to be responsible of the tension with the data. Motivated by an SO(10) grand unified theory with an intermediate Pati-Salam theory, we then focus on one of the scenarios preferred by the effective field theory fit, namely the one with a scalar leptoquark S${}_1$. We update the evaluation of the effects of this particle on the coupling of leptons to the Z gauge boson, including effects coming from electroweak renormalisation, and include the Z-pole observables in the fit of the Yukawa coupling to b→c$\ell$ν data. Finally, we discuss in more detail the possible UV completion of a model containing the scalar leptoquark S${}_1$.