Measurement of $D^0-\overline{D^0}$ mixing parameters and search for $CP$ violation in $D^0 \rightarrow K^+ \pi^-$ decays with LHCb Run 2 data

$D^0-\overline{D^0}$ mixing parameters are measured in the decay-time-dependent ratio of $D^0 \rightarrow K^+ \pi^-$ to $D^0 \rightarrow K^- \pi^+$ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of $5.9\,\text{fb}^{-1}$ collected by LHCb experiment from 2015 to 2018 at the center-of-mass energy of $13$ TeV. The strong-interaction decay $D^{*\pm} \rightarrow D^0 \pi^{\pm}$ is used to infer the flavour of the D0 meson at production, then the measurement is performed separately for $D^0$ and $\overline{D^0}$ yielding a direct $CP$-violating asymmetry. Error estimation is determined, showing an improvement of about $35\%$ with respect to the previous LHCb analysis.