Measurements of Charmonia Production and a Study of the X(3872) at LHCb

The LHCb experiment at the Large Hadron Collider (LHC) at CERN has been running successfully for the last three years. The Ring Imaging Cherenkov (RICH) sub-detectors provide the particle identification for the LHCb experiment. During the 2010 and 2011 runs the muon identification efficiency has been successfully used to monitor the RICH performance both on-line and off-line. Charmonium production in collisions with high energy hadrons provides precise tests of theoretical models based on Quantum ChromoDynamics (QCD). The $\chi_c$ mesons are identified through their decay $\chi_c \rightarrow \mathrm{J}/\psi \gamma$ with $\mathrm{J}/\psi \rightarrow \mu^+ \mu^-$ using $\sim$ 35.6 pb$^{-1}$ of data collected by the LHCb detector in 2010. The ratio of the prompt cross-sections for the two $\chi_c$ spin states, $\sigma_{\chi_{c2}} / \sigma_{\chi_{c1}}$, and the ratio of the prompt cross-sections $\chi_c \rightarrow J/\psi \gamma$ and J/$\psi$, $\sigma_{\chi_{c}} / \sigma_{J/\psi}$, have been determined as a function of the J$\psi$ transverse momentum ($p_{T}^{J/\psi}$) in the range 2 to 15 GeV/$c$. The variation of $\sigma_{\chi_{c2}} / \sigma_{\chi_{c1}}$ with $p_{T}^{J/\psi}$ is in agreement with the Colour Singlet (CS) model but the results are not precise enough to rule out sizeable Colour Octet (CO) terms. The $\sigma_{\chi_{c}} / \sigma_{J/\psi}$ results are in excellent agreement with NRQCD expectations but there are large discrepancies with the CS description. Another open question in the charmonium model is related to the nature of the X(3872) particle. The measurement of the $J$ and $P$ quantum numbers of the X(3872) at LHCb through an angular analysis of the B$_u^+ \rightarrow$ X(3872)$(\rightarrow J/\psi(\mu^+\mu^-)\rho(\pi^+\pi^-))\, K^+$ decay has been discussed in this thesis. The reconstruction and selection of these events has been studied using the full LHCb MC simulation. With a 2 fb$^{-1}$ data set, 2478 $\pm$ 519 B$^+_u \rightarrow X(3872) K^+$ events are expected at $\sqrt{s}$ = 10 TeV with a background to signal ratio of 0.23 $\pm$ 0.06. The angular distribution functions have been calculated. In order to distinguish between the two possible $J^{PC}$ hypotheses (1$^{++}$ and 2$^{-+}$) at a 3(5)$\sigma$ level, a minimal integrated luminosity of 2.2 fb$^{-1}$(6.9 fb$^{-1}$) at $\sqrt{s}$ = 7 TeV and 0.14 fb$^{-1}$ (0.43 fb$^{-1}$ at $\sqrt{s}$ = 10 TeV to be collected at LHCb.