Thesis defense of Fabio De Vellis

Symmetries in the Standard Model of particle physics stem from fundamental aspects of the theory and play a determinant role in shaping our understanding of elementary particles. Isospin symmetry predicts nearly identical decay rates for processes differing only by a spectator quark, such as the rare decays B0 -> K0 mu+ mu- and B+ -> K+ mu+ mu-. The isospin asymmetry, defined as the difference in their partial widths, is a theoretically clean observable: dominant hadronic uncertainties cancel out, offering a precise test of the theory.

Previous measurements have hinted at coherent deviations from the Standard Model expectations, motivating a more precise determination using a larger dataset. This thesis details the complete strategy for an updated measurement of the differential branching fractions and isospin asymmetry of these decays, using the full proton-proton collision dataset collected by the LHCb experiment during Run 1 and Run 2, corresponding to 9/fb. The analysis is performed in intervals of the dimuon invariant mass squared, using the resonant decays B -> J/psi K as normalisation to reduce systematic uncertainties.

A blinded approach is adopted to prevent experimenter bias. Consequently, while the final numerical results are not included, this thesis details the comprehensive analysis strategy. All key aspects are presented, including the optimisation of the event selection, the calibration of the simulation, and the development of the simultaneous fitting framework. The robustness of the method is demonstrated through extensive validation using control modes and pseudo-experiments. Finally, the expected sensitivity of the measurement is evaluated, highlighting the potential of the full dataset to significantly improve the precision compared to previous results.