Study of Rare Charm Decays with the LHCb Detector at CERN

Rare charm decays proceed mostly through the $c\rightarrow u$ Flavor Changing Neutral Current (FCNC), which is possible only at loop level in the Standard Model (SM). In charmed decays, FCNCs are subject to a very efficient GIM suppression leading to very rare processes. Consequently, rare charm decays are good tools to probe New Physics (NP) beyond the SM. NP particles could become detectable by causing observables such as branching ratios and CP or angular asymmetries to deviate from the SM predictions. The main subject of this thesis is the measurement of the branching ratio of the $D^{0}\rightarrow K^{-}\pi^{+}\rho/\omega(\rightarrow\mu^{+}\mu^{-})$, the partial branching ratio of the of the $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$ mode, in the region of the $m(\mu^{+}\mu^{-})$ dominated by the $\rho$ and $\omega$ resonances: 675 MeV/$c^{2} < m(\mu^{+}\mu^{-}) <$ 875 MeV/$c^{2}$. It will be precious in the future, in particular as a normalisation mode in the study of all: $D^{0}\rightarrow h^{\pm}h^{(')\mp}\mu^{+}\mu^{-}$ decays $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$, $D^{0}\rightarrow \pi^{+}\pi^{-}\mu^{+}\mu^{-}$, $D^{0}\rightarrow K^{+}K^{-}\mu^{+}\mu^{-}$ and $D^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$. Using 2fb$^{-1}$ of 2012 LHCb data we find: \begin{equation*} {B}(D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-})=(4.37\pm 0.12_{stat.}\pm 0.53_{sys.})\times 10^{-6}. \end{equation*} This is the first measurement of this mode. We also determined sensitivities to total and partial branching fractions and asymmetries in $D^{0}\rightarrow h^{\pm}h^{(')\mp}\mu^{+}\mu^{-}$ decays with future LHCb datasets. In addition, the systematic uncertainties affecting the searches for the 3-body decays, $D^{+}_{(s)}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ and $D^{+}_{(s)}\rightarrow\pi^{-}\mu^{+}\mu^{+}$, carried out by LHCb based on the data collected in 2011 (1 fb$^{-1}$). Finally, the results of the tests of front-end electronic board for the Upgrade of LHCb are presented.