Measurement of CP Violation using $B^0 \rightarrow D^{(*)\pm}D^{\mp}_{(s)}$ decays at LHCb

This thesis presents two measurements, performed using data collected by the LHCb experiment, operating at the Large Hadron Collider accelerator at CERN. The first is the measurement of the CP violation observables $S$ and $C$ in the decays of $B^0$ and $\bar{B}^0$ mesons to the $D^+D^-$ final state exploiting a data sample corresponding to an integrated luminosity of 3 $fb^{-1}$ collected in proton-proton collision at center of mass energies of 7-8 TeV, and resulting in \[S_{D^+D^-} = -0.54^{+0.17}_{-0.16}(stat) \pm0.05(syst)\] \[C_{D^+D^-} = 0.26^{+0.18}_{-0.17}(stat) \pm0.02(syst)\] This result combined with the constraint coming from $B^0 \rightarrow J/\psi K^0_s$ measurements, allows to constrain the phase shift $\Delta \phi$ to world's most precise value of $\Delta \phi$=-0.16$^{+0.19}_{-0.21}$ rad, implying only small contribution from higher-order Standard Model corrections. The second aims to measure the CP violation observables $S_{D^{\star}D}$, $C_{D^{\star}D}$, $\Delta S_{D^{\star}D}$ and $\Delta C_{D^{\star}D}$ in the decays of $B^0$ and $\bar{B}^0$ mesons to the $D^{\star+}D^-$ final state using a data sample corresponding to an integrated luminosity of 5 $fb^{-1}$ collected at the LHCb experiment in proton-proton collision at center of mass energies of 7-8 TeV and 13-14 TeV, using a flavour-tagged, decay-time dependent analysis. From the preliminary results obtained it is possible to estimate the expected sensitivity for the CP observables to be \[\sigma_{S_{D^{\star}D}} = 0.09 \hspace{3cm} \sigma_{\Delta S_{D^{\star}D}}=0.09\]