A novel method for searching for $C\!P$ violation in the $D^0 \to K^0_s K^{\pm}\pi^{\mp}$ decays with LHCb Run 2 data

This thesis presents the most recent studies of the D*-tagged $D^0 \to K_S^0 K^\pm \pi^\mp$ decay channels, using the LHCb data sample collected during the LHC Run~2. The core of the work consists in the design and implementation of a novel and robust analysis methodology that aims at measuring the time-integrated CP asymmetry ($A_{CP}$), both by integrating over the entire phase space and in a restricted region, such as in the vicinity of the $K^*(892)^0 K^+ \pi^- $ resonance. The driving idea of the method exploits the cancellation of all nuisance asymmetries by means a double $\Delta A_{CP}$ mechanism between decay modes with very similar kinematics, and collected with very similar selections. The full data sample collected by the LHCb experiment during the LHC Run 2, corresponding to an integrated luminosity of about 5.6 fb-1, is used. Thanks to the optimized selection, the final sample is very pure allowing for the first time the measurement of the $A_{CP}(D^0 \to K_S^0 K \pi) $ at a unprecedented level of about 1x10-3. The study reported in this thesis returned to be very robust, since a double $\Delta A_{CP}$ difference mechanism is exploited to search for possible hints of CP-violating asymmetries in the $D^0 \to K_S^0 K^\pm \pi^\mp$ decays. It paves the way for a measurement with the already available Run~2 data sample at the per mil level, and for future measurements, at much higher statistics, in the Upgraded LHCb era.