CP Violation in $B^\pm\to D h^\pm$ Decays where $D\to K^0_{\rm S} h'^+h'^-$

This thesis presents a measurement of the Cabibbo-Kobayashi-Maskawa angle $\gamma$ using $B^\pm\to D K^\pm$ and $B^\pm\to D \pi^\pm$ decays, where the D meson decays to one of the final states $K^0_{\rm S} \pi^+\pi^-$ and $K^0_{\rm S} K^+K^-$. The measurement relies on the distribution of signal decays over the phase space of the $D$ decay, analysed using a model-independent method based on strong-phase measurements by the CLEO and BESIII collaborations. The measurement is performed using proton-proton collision data collected by the LHCb experiment during the full Run 1 and 2 of the Large Hadron Collider, corresponding to a total integrated luminosity of $8.7\,\text{fb}^{-1}$ at centre-of-mass energies of $\sqrt s =7$, $8$, and $13 TeV$. The measurement determines that $\gamma= (68.7^{+5.2}_{-5.1})^\circ$, with an alternative solution corresponding to $\gamma+180^\circ$. This is the most precise stand-alone measurement of $\gamma$ to date, and achieves a precision that is comparable to all earlier measurements of $\gamma$ combined. The thesis also presents a phenomenological study of the impact of neutral kaon CP violation and material interaction on $\gamma$ measurements with ${B^\pm\to (K^0_{\rm S} h^+h^-)_D h'^\pm}$ decays. The existing literature at the outset of the thesis work had estimated the potential bias to be $\mathcal O(1^\circ)$ in $B^\pm\to D K^\pm$ decays and to scale with $1/r_B$. This suggests potentially large biases for a measurement with $B^\pm\to D \pi^\pm$ decays, since $r_B^{D\pi}\simeq0.005$ is much smaller than $r_B^{DK}\simeq 0.1$. However, the thesis argues that the actual impact is an order of magnitude smaller, as long as the $CP$-violation observables are determined based on the phase-space distribution of signal decays. This is demonstrated in a number of numerical studies that take the geometries of the LHCb and Belle~II detectors into account.