Measurement of $D^{0}-\overline{D}^{0}$ mixing and search for CP violation in $D^{0}\toK^{\pm}\pi^{\mp}$ decays at LHCb

The oscillations of neutral mesons are a manifestation of the fact that mass eigenstates are a superposition of flavour eigenstates. Since they belong to the class of \textit{flavour changing neutral current} processes, they cannot be mediated at tree level in the Standard Model and thus constitute a powerful probe of new physics at high energy scales. Violation of the charge-parity symmetry may lead to different mixing rates for a particle produced as a meson or as an anti-meson. The observation of large CP asymmetries would also be a hint of physics beyond the Standard Model. The LHCb experiment, located at the Large Hadron Collider at CERN, has been designed to perform precision measurements of the decays involving the \textit{beauty} and \text{charm} quark. In charm physics, the LHCb experiment realized important measurements, such as the first observation of neutral charmed mesons oscillations ($D^0$) from a single measurement. Here, oscillations are suppressed and CP violation is expected to be tiny ($\sim\mathcal{O}(10^{-3})$) within the SM. This thesis aims to measure the charm mixing parameters and search for CP violation with the decay-time-dependent ratio of $D^0\to K^+\pi^-$ to $D^0\to K^-\pi^+$ rates and charge conjugate processes. The datasets used in the analysis were recorded by LHCb during 2015 and 2016 in proton-proton collisions at $\sqrt{s}=13\,\text{TeV}$, corresponding to an integrated luminosity of $0.3\text{fb}^{-1}$ and $1.6\text{fb}^{-1}$, respectively. In the limit of CP symmetry, the mixing parameters are determined to be $x'^2=(0.100\pm 0.027 \pm 0.010)\times 10^{-3}$, $y'=(4.086\pm 0.52 \pm 0.20)\times 10^{-3}$ and $R_{D}=(3.553\pm 0.031\pm 0.010)\times 10^{-3}$, where the first uncertainty is statistical and the second systematic, respectively. When the measurement is performed separately for $D^0$ and $\Dzb$ mesons, there is no evidence for CP violation.