$CP-$violation in Partially Reconstructed $B^\pm \rightarrow \ D^*h^\pm$Decays at LHCb

This thesis presents a measurement of $CP-$violation in partially reconstructed $B^\pm \rightarrow \ D^*K^\pm$ and ${B^\pm \to D^* \pi^\pm}$ decays, where the neutral pion and photon from the $D^* \to D\pi^0$ and ${D^* \to D \gamma}$ decays are not reconstructed. The $D$ meson is subsequently reconstructed in the ${D \to K^{^0_S} \pi^+ \pi^-}$ or $D\to K^{^0_S} K^+K^-$ final state. The measurement of $CP-$violation is performed by analysing the distribution of the signal yields over the $D-$decay phase space, without relying on a $D-$decay amplitude model. Instead, inputs for strong phase-related parameters measured at $\text{CLEO}$ and $\text{BESIII}$ are used. The measurement is performed using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 $TeV$, with a total integrated luminosity of approximately 9 fb$^{-1}$. The work in this thesis measures $CP-$violating observables using partially reconstructed $B^\pm \rightarrow \ D^*K^\pm$ and ${B^\pm \to D^* \pi^\pm}$ decays at LHCb. These observables are interpreted in terms of physical parameters, including the Cabibbo-Kobayashi-Maskawa angle, $\gamma$, a fundamental Standard Model parameter. This is found to be ${\gamma = (92^{+21}_{-17})^\circ}$, where the total uncertainty includes the statistical and all systematic uncertainties.