Updated determination of $D^0-\overline{D}^0$ mixing and $C\!P$ violation parameters with $D^0 \to K^+\pi^-$ decays

The first observation of $D^0-\overline{D}^0$ mixing from a single experiment was reported by LHCb already six years ago. Since then, experimental efforts have been focussing on improving the knowledge of the mixing parameters and searching for $C\!P$-violating effects in mixing. In this seminar we report on the latest measurements of charm-mixing parameters based on the decay-time-dependent ratio of $D^0 \to K^+\pi^-$ to $D^0 \to K^-\pi^+$ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of $5.0\,\mathrm{fb}^{-1}$ recorded by the LHCb experiment from 2011 through 2016. Assuming $C\!P$ symmetry, the mixing parameters are determined with unprecedented precision. Without this assumption, the measurement is performed separately for $D^0$ and $\overline{D}^0$ mesons, yielding the direct $C\!P$-violating asymmetry and the magnitude of the ratio of mixing parameters |q/p|. No evidence for $C\!P$ violation in charm mixing is observed yet, but the quest is progressing.