Neutral kaon detection asymmetry with charm hadron decays at LHCb

This thesis presents a high precision measurement of the asymmetry in detecting neutral kaons, $K^0$ and $\overline{K}^0$, produced in charm hadrons decays. The analysis utilises data from $pp$ collisions at a centre-of-mass energy of 13 TeV, collected with the LHCb detector during Run 2 (2016- 2018). The dataset includes approximately 50 million $D^+ \to K_S^0 \pi^+$ signal candidates and 30 million $D^+ \to\phi \pi^+$ signal candidates. This work is relevant for the search for CP-violating asymmetries in charm hadron decays. Precisely determining all charge asymmetric contributions, such as production and detector-induced effects, is essential to accurately measure CP violation. This is achieved by exploiting specific calibration channels, some of which include a neutral kaon in the final state. This thesis models and quantifies the contribution to the neutral kaon detection asymmetry arising from the interference between the Cabibbo-Favoured and Doubly Cabibbo-Suppressed harm hadron decay amplitudes to final states containing a neutral kaon. These effects are studied in the $D^+ \to K_S^0 \pi^+$ decay mode and they can be parameterised by the ratio of the DCS to CF amplitudes, in particular by the modulus $r_\pi$ and the relative strong phase $\delta_\pi$, defined as $$\frac{\mathcal{A}(D^+ \to K^0\pi^+)}{\mathcal{A}(D^+ \to \overline{K}^0\pi^+)} \equiv r_\pi \ e^{i\delta_\pi}\,.$$ This contribution has a significant impact, especially at high neutral kaon decay times, and can no longer be neglected in current and future high-precision measurements. The relevant parameters describing this interference, $r_\pi$ and $\delta_\pi$, are measured for the first time directly from data. Additionally, this thesis presents the measurement of the direct CP asymmetry in the $D^+ \to \phi \pi^+$ channel with the full LHCb Run 2 dataset, using $D^+ \to K_S^0 \pi^+$ as a calibration channel. Thanks to the determination of $r_\pi$ and $\delta_\pi$, $D^+ \to K_S^0 \pi^+$ decays with neutral kaons reconstructed outside the acceptance of the vertex detector are included in the analysis, allowing a more robust estimate of systematic uncertainties related to the knowledge of the neutral kaon detection asymmetries.