Model-independent measurement of the CKM angle $\gamma$ in $B^\pm \to [h^+h^-\pi^+\pi^-] _Dh'^\pm (h = K , \pi)$ decays at LHCb and BESIII

This thesis describes two complementary analyses related to the four-body $D^0\to K^+K^-\pi^+\pi^-$ and $D^0\to\pi^+\pi^-\pi^+\pi^-$ decays, where the ultimate objective is to study $C\!P$ violation and measure the CKM angle $\gamma$. First, a model-independent determination of parameters describing the strong-phase difference between the $D^0$ and $\bar{D}^0\to K^+K^-\pi^+\pi^-$ decays is performed. The analysis uses a sample of quantum-correlated $D\bar{D}$ pairs produced in $e^+e^-$ collisions at the $\psi(3770)$ resonance. The data sample corresponds to an integrated luminosity of $16$fb$^{-1}$, recorded by the BESIII detector. The measurement is performed in bins of phase space, using a five-dimensional binning scheme optimised for sensitivity to $\gamma$. In the second part, a sample of $pp$ collisions collected by the LHCb detector, corresponding to $9$fb$^{-1}$ of integrated luminosity, is used to obtain a model-independent measurement of $\gamma$ with the $B^\pm\to D h^\pm$ decay, where $h = K$ or $\pi$. The neutral charm meson subsequently decays to the four-body $D\to K^+K^-\pi^+\pi^-$ or $\pi^+\pi^-\pi^+\pi^-$ modes. This is the first binned measurement of $\gamma$ using these multi-body decays, utilising strong-phase parameters from BESIII as external inputs. Additionally, a study of the phase-space integrated $C\!P$-violating effects is also performed. The result is $\gamma = (53.6_{-6.7}^{+8.6})^\circ$, which is a combination of both phase-space binned and phase-space integrated $C\!P$-violating observables. It is one of the most precise stand-alone measurements of the CKM angle $\gamma$. The uncertainties are currently statistically dominated.