Searching for confirmation of charm CP violation in $K^0_S$ final states at LHCb

This thesis reports a measurement of the CP asymmetry in $D^0 \to K^0_S K^0_S$ decays, based on $pp$ data collected by LHCb at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.7 fb${^-1}$. The $D^{*+} \to D^0 \pi^+$ decay is used to infer the flavour of the $D^0$ meson at production. The $D^0 \to K^+ K^-$decay, which has a well measured CP asymmetry, is used as a calibration channel. The time-integrated CP asymmetry for the $D^0 \to K^0_S K^0_S$ decay is measured to be: $$A^{CP}(D^0 \to K^0_S K^0_S) = (-3.1\pm 1.2\pm 0.4 \pm 0.2 )\%, $$ where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the asymmetry of the calibration channel. This is the most precise determination of this quantity to date and it is still compatible, albeit marginally, with zero asymmetry. In view of further measurements in future runs of LHCb, a study of the performance of an innovative real-time tracking system based on FPGAs is presented. This system is designed to process events at the full LHC collision rate of 30 MHz, with the aim of significantly increasing the trigger efficiency for the $D^0 \to K^0_S K^0_S$ decay channel and other relevant charm modes.