The RICH detectors for the LHCb experiment and a study of charmless three-body B decays

This thesis deals with the capability of identifying charged hadrons at LHCb, in the present and in the future. Particle identification of charged hadrons is a fundamental requirement of the LHCb experiment in order to fulfill its physics programme and it is mainly provided by two Ring Imaging Cherenkov detectors. The Ring Imaging Cherenkov sub-detectors have been operating successfully since the beginning of the LHC data taking in 2009. The calibration and the alignment of the RICH detector are fundamental to be able to reconstruct the Cherenkov angle associated with the individual photons as accurately as possible. The magnetic distortion correction procedure for RICH2, described in this thesis, is able to correct the magnetic distortion effects on the photoelectron trajectories inside the photodetectors and restore the nominal resolution of the Cherenkov angle. A procedure to align the HPD inside the HPD plane has been also studied to correct the misalignments between the HPD. The separation between kaons, pions and protons is fundamental also in the study of charmless three-body $B^{\pm} \to p \bar p K^{\pm}$ decays. The channel and its intermediate substructures have been studied. Based on a sample of $(6951 \pm 176)$ of $B^{\pm} \to p \bar p K^{\pm}$ decays reconstructed in $1.0\,{\rm fb^{-1}}$ of data collected with the LHCb detector, the relative branching fractions are measured to be \begin{align*} \frac{{\mathcal B}(B^{+} \to p \bar p K^{+})_{\rm total}}{{\mathcal B}(B^{+} \to J/\psi K^{+} \to p \bar p K^{+})}=& \, 4.91 \pm 0.19 \, {(\rm stat)} \pm 0.15 \,{(\rm syst)},\\\frac{{\mathcal B}(B^{+} \to p \bar p K^{+})_{M_{p\bar p < 2.85} \,{\rm GeV/}c^{2}}}{{\mathcal B}(B^{+} \to J/\psi K^{+} \to p \bar p K^{+})}=& \, 2.02 \pm 0.10 \,{(\rm stat)}\pm 0.08 \, {(\rm syst)},\\\frac{{\mathcal B} (B^{+} \to \eta_{c} K^{+} \to p\bar p K^{+})}{{\mathcal B}(B^{+} \to J/\psi K^{+} \to p\bar p K^{+})} = & \, 0.578 \pm 0.035 \, {(\rm stat)} \pm 0.025 \, {(\rm syst)},\\\frac{{\mathcal B} (B^{+} \to \psi(2S)K^{+} \to p\bar p K^{+})}{{\mathcal B}(B^{+} \to J/\psi K^{+} \to p\bar p K^{+})}=& \, 0.080 \pm 0.012 \, {(\rm stat)} \pm 0.010 \, {(\rm syst)}.\\\end{align*} Upper limits on the $B^{+}$ branching fractions into the charmonium resonances $\eta_{c}(2S)$ and $h_{c}$ and into the charmonium-like states $X(3872)$ and $X(3915)$ are also obtained. An upper limit on the ratio \begin{equation*} \frac{{\mathcal B} (X(3872) \to p \bar p)}{{\mathcal B} (X(3872) \to J/\psi \pi^{+} \pi^{-})}< 2.0\times 10^{-3} \end{equation*} is derived. The upper limit of this ratio is already challenging some of the predictions for the molecular interpretations of the $X(3872)$ state and it is approaching the range of predictions for a conventional $\chi_{c1}(2P)$ state. The current particle identification system shows some limitations in an upgrade environment, where the plan is to take data at a luminosity of $1 \times 10^{33} \,{\rm cm^{-2}s^{-1}}$. A study of a new detector for particle identification of charged hadrons of low momentum for the LHCb upgrade has been performed. The novel detector, the TORCH, combines time-of-flight and RICH detection technique. The preliminary results from photodetectors and readout electronics performed both in laboratory and in test beam show a good performance, not too far away from the requirements on the time resolution. Further investigation and R$\&$D are necessary and planned in the near future.