Charmonium production at LHCb: measurement of the $\psi'$ to $J/\psi$ production ratio with the first data

LHCb is an experiment dedicated to precise measurements of CP violating and rare decays of $b$-hadrons. It will exploit the proton-proton collisions at an energy of 14 TeV in the centre-of-mass system, produced by the LHC collider (CERN-Geneva), and will operate at a luminosity of $2 x 10^{32} cm^{-2}s^{-1}$. The expected number of pairs $b\overline{b}$ produced by the LHC collisions is $N_{b\overline{b}}\approx 10^{12}/year$. LHCb is designed with a robust and efficient trigger whose purpose is to reduce the event rate in input ($\approx10 MHz$) to a manageable event rate, enriched in content of heavy flavour quarks, to be written to storage ($\approx 2kHz$). The rate reduction is achieved in two trigger levels, L0 (Level 0) and HLT (High Level Trigger), that will be widely discussed in this thesis. A good particle identification as well as efficient tracks and vertexes reconstruction, are fundamental requirements for the reconstruction of the $b$-hadron decays and proper time measurement. LHCb aims to improve the current precision on the CKM parameters and to search for any possible inconsistency with the Standard Model predictions in order to find out eventual "New Physics" effects. The LHCb detector is fully installed, commissioned and ready for data taking: the LHC start-up is expected by the end of 2009. In the first periods of data taking, the understanding of the apparatus, as well as the preparatory measures, are necessary steps for the future analyses on the $b$-hadrons. In particular the charmonium states will be largely produced either as prompt or from $b\to c$ transitions.Their well known properties make these resonances ideal for alignment and calibration studies. On the other hand the observation of charmonium states and the measurement, per example, of the prompt cross section ratio between $\psi(2S)$ and $J/\psi$ can give some interesting informations about the production mechanisms. The hadroproduction of $J/\psi$ and $\psi(2S)$ is not yet completely understood. Early models could not describe the cross section of directly produced $J/\psi$ mesons. Such models underestimated the measurements by a factor of approximately 50 and did not adequately describe the cross section shape as a function of $p_T$. With the advent of Non-Relativistic QCD (NRQCD) it has been possible to give a better theoretical description of charmonium production through the introduction of the Color Octet model. Nevertheless there are still a lot of issues and open problems: the spin alignment of $psi$ mesons predicted by NRQCD theories is totally in disagreement with the CDF findings (polarization puzzle); moreover recent NL0 and NNL0 calculations in the Color Singlet model have shown that the amount of the Color Octet needed so far to explain data could be overestimated. Further measurements with $J/\psi$ and other charmonia states are needed to discriminate between the models and clarify the situation. In this thesis the measurement of the prompt cross section ratio between $\psi(2S)$ and $J/\psi$, with the first data of LHCb, is described. Simulation studies have been performed to assess the acceptances, the efficiencies and the systematic errors introduced by the apparatus. Particular emphasis is given to the polarization of the $\psi's$ and to the systematic induced. This measure is a starting point for the subsequent absolute cross section measurements. In chapters I-II-III of this thesis essentially we give a detailed description of the LHCb experiment including the trigger and the online monitoring system. In chapter IV we discuss the theory of charmonium production and the expectations at LHCb. In the chapters V-VI, we present a study on Monte Carlo data in which the measurement of the prompt cross section ratio between $\psi(2S)$ and $J/\psi$, in the dimuon channel, is described. Finally, in the chapter VII we will discuss some further prospects on charmonium measurements.