Model-independent measurement of charm mixing parameters in $D^0 \rightarrow K_S^0 \pi^+ \pi^-$ decays

This thesis presents a measurement of charm mixing and CP-violation parameters using $D^0 \rightarrow K_S^0 \pi^+ \pi^-$ decays. These mixing parameters include the mass and decay-width differences of the mass eigenstates of the $D^0$-$\overline{D}^0$ system. A search for Charge-Parity violation is performed through measurements of $D^0$-$\overline{D}^0$ mixing and of the interference between mixing and decay amplitudes. The dataset consists of events reconstructed in $pp$ collisions collected by the LHCb experiment during the operation of the Large Hadron Collider (LHC) from 2016 to 2018. This sample corresponds to an integrated luminosity of 5.4 fb$^{-1}$. The $D^0$ decays are selected in semileptonically decays of $b$ hadrons. The results are expressed in terms of the CP-averaged mixing parameters and CP-violating differences as \begin{align*} x_{\rm CP} &= [ \,\,\,\,\,4.29 \pm 1.48 \mbox{(stat)} \pm 0.26 \mbox{(syst)} ] \times 10^{-3}\,,\\ y_{\rm CP} &= [ \,\,12.61 \pm 3.12 \mbox{(stat)} \pm 0.83 \mbox{(syst)} ] \times 10^{-3} \,,\\ \Delta x \,\, &= [ \,-0.77 \pm 0.93 \mbox{(stat)} \pm 0.28 \mbox{(syst)} ] \times 10^{-3} \,,\\ \Delta y \, &= [ \,\,\,\,\,3.01 \pm 1.92 \mbox{(stat)} \pm 0.26 \mbox{(syst)} ] \times 10^{-3} \,. \end{align*} where the first uncertainty is statistical and the second is systematic. They correspond to the mixing and CP-violation parameters \begin{align*} x &= 0.46^{+0.15}_{-0.16}\times10^{-2} \,, \\ y &= 1.24^{+0.32}_{-0.33}\times10^{-2} \,, \\ |q/p| &= 1.21^{+0.21}_{-0.15} \,,\\ \phi &= -0.132^{+0.088}_{-0.120} \, \mbox{rad}. \end{align*} The value of $x$ deviates from zero with a significance of almost 3$\sigma$. These results are complementary to and consistent with previous measurements and with the current world-average values. They represent an independent and complementary knowledge of the charm-mixing parameters. A combination with the recent LHCb analysis of $D^{*+} \rightarrow D^0 ( \rightarrow K_S^0 \pi^+ \pi^-) \pi^+ $ decays is also reported.