Radiation hardness of the upgraded LHCb muon detector electronics and prospects for a full angular analysis in multi-body rare charm decays

In this dissertation the results of the studies on the new readout electronics for the muon system of the LHCb experiment, and the perspectives for carrying out a full angular analysis in the rare decays $D^{0}\to \pi^+ \pi^- \mu^+ \mu^-$ and $D^{0}\to K^+ K^- \mu^+ \mu^-$ will be described. The LHCb experiment studies the heavy hadron physics, containing charm or bottom quarks, in particular searching for new Charge-Parity ($C\!P$) symmetry violation sources, searching for rare decays and studying their properties. LHCb produced leading results in these fields so far. In order to obtain more precise measurements or be able to study new observables, many analyses need a considerable increase in statistics, thus the experiment is now being upgraded to run with an higher instantaneous luminosity of proton-proton collisions. For this reason the readout electronics has been completely replaced by a new optimised version. Several tests have been performed on the new readout electronics that will be here discussed, and that have allowed a comprehensive radiation hardness characterization of the UMC 130 nm technology, used to develop the main electronics device of the muon system readout electronics, the nSYNC chip. On the other hand, in the last two years of data taking, 2017 and 2018, an excellent performance of the LHCb experiment has been obtained and the significant increase in statistics allowed access to new observables, especially in the field of rare decays. In particular, it has been possible to increase the statistics of rare four-body charm decays, like $D^{0}\to \pi^+ \pi^- \mu^+ \mu^-$ and$D^{0}\to K^+ K^- \mu^+ \mu^-$ , of which LHCb already carried out the branching fractions measurement, as well as of angular and $C\!P$ asymmetries. Since interesting results and flavour anomalies have already been obtained from angular analyses of rare $B$ decays, it is important to study the possibility of these analyses in the complementary sector of rare charm decays. In this work the perspectives for performing a full angular analysis with $D^{0}\to \pi^+ \pi^- \mu^+ \mu^-$ and $D^{0}\to K^+ K^- \mu^+ \mu^-$ decays will be discussed. An angular analysis will allow to carry out several Standard Model tests in the field of rare $D$ decays, allowing also to measure theoretically clean observables for probing effects of physics beyond Standard Model, that can occur at high energy scale.