Abstract
Despite its tremendous success, the Standard Model (SM) of particle physics is incomplete, as various observations provide conclusive evidence of physics beyond the Standard Model (BSM). A notable example is the discovery of neutrino masses and oscillations, which clearly indicate that lepton flavour is not a symmetry of nature, thus demanding an extension of the Standard Model. Lepton Flavor Violation (LFV), defined as short-range flavour-changing interactions among the charged leptons, is expected to occur but it is yet to be observed. The new generation of experiments aimed at detecting lepton flavour-changing transitions will provide unprecedented experimental sensitivities and further probe LFV new physics.In this thesis, we assume that LFV physics is heavy and parametrize its effects using the Standard Model Effective Field Theory (SMEFT). LFV interactions are described by higher-dimensional operators constructed out-of-the SM fields, and observables are computed in terms of the operator coefficients.First, we introduce a small power counting parameter à la Wolfenstein to asses whether the state-of-the-art SMEFT calculations, which include the dimension six operators and their one-loop renormalization group equations, are sufficient to have a complete effective description of LFV observables. We find that the upcoming searches of muto e can be sensitive to a few dozen dimension eight operators, and to some effects of two-loop anomalous dimensions, for new physics scales respectively below 20-100 TeV.We build on these results and explore the sensitivity of muto e searches to tauleftrightarrow e(mu) flavour changing interactions. We describe the tauleftrightarrow e(mu) interactions as dimension six operators in the SM EFT, identify pairs of them giving interesting contributions to muto e processes, and obtain the anomalous dimensions mixing those pairs into dimension eight muto e operators. The dimension eight operator renormalization is mostly unknown, and we computed a subset of renormalization group equations for the first time. We show that upcoming muto e experiments could allow to probe parameter space beyond the reach of current and future searches of tauto e(mu) transitions, including Higgs, tau and B meson decays.