Identificazione di particelle e studio del decadimento $B^{\pm} \rightarrow K^{\pm} \pi^{0}$ con il rivelatore RICH di LHCb

The violation of the CP symmetry is one of the still open issues in the physics of fundamental interactions. Moreover, CP violation is important to understand the asymmetry between matter and anti-matter in the universe. LHCb is one of the experiments installed at the Large Hadron Collider (LHC) at CERN, and it is dedicated to precise measurements of CP violation and rare decays in the B hadron sector to test flavour physics in the Standard Model and to point out possible New Physics beyond the Standard Model. One of the key aspects of LHCb is the identification of the B decay products. The capability to distinguish between a pion and a kaon in the final state is fundamental to measure CP violation. This identification is provided by two RICH (Ring Imaging CHerenkov) detectors covering the particle momentum range 1 $\div$ 100 GeV/$c$. Cherenkov photons are detected using Hybrid Photon Detector (HPD). My thesis deals with three topics: characterization and correction of the magnetic distortion effects on the HPD; spatial HPD alignment; preliminary study of the decay channel $B^{\pm} \rightarrow K^{\pm}\pi^{0}$. HPD must operate in the fringe field of the LHCb dipole. Photo-electron trajectories are deviated by the Lorentz force with respect to the nominal ones. This produces a distortion effect of the image on the HPD anode. The distortion, if not corrected, even if it is small, can increase the error on the Cherenkov angle meas urement and can deteriorate the particle identification capability, that is fundamental for the physics programme at LHCb. For this reason it is necessary to study and correct this distortion, implementing an offline procedure to restore the nominal resolution. Measurements of a known light pattern projected onto the HPD matrix has been performed with and without magnetic field to evaluate the effect. An algorithm capable to reconstruct the position of the pattern points and to parametrise the distortion has been implemented. The distortion has been corrected and the obtained residual uncertainty is smaller than the one due to the pixel size. The same measurements have been used both to study magnetic distortion effects and to align the HPD. The projected pattern of light points, can be used to verify if there are misalignments among the HPD. A fit algorithm has been developed to correct misalignments. The obtained resolution is smaller than the one due to the pixel size. Charmless decays are important for the LHCb physics program to study CP violation. The $B^{\pm} \rightarrow K^{\pm}\pi^{0}$ decay is interesting and shows direct CP violation. An asymmetry: $A_{CP}$ = 0.051 $\pm$ 0.025 has been measured by the BaBar, Belle and CLEO experiments. Moreover an asymmetry of $A_{CP}$ = -0.098 $\pm$ 0.013 has been measured by the same experiments for the $B^0 \rightarrow K^{\mp} \pi^{\pm}$ channel. On theoretical grounds one would ex pect that the two asymmetries are about equal. This discrepancy gives rise to the so-called “$K-\pi$ puzzle". In order to understand the origin of this discrepancy both further theoretical developments and more precise experimental measurements are necessary. A preliminary study has been performed to reconstruct the $B^{\pm} \rightarrow K^{\pm}\pi^{0}$ channel decay at LHCb using Monte-Carlo data. A fit algorithm to find the secondary vertex has been developed. A selection using kinematic variables and taking into account the channel topology has been used. Efficiency and purity of the selection have been evaluated.