Study of direct production and polarization measurement of $J/\psi$ at the ATLAS experiment

The ATLAS B-physics program covers many aspects of charm and beauty flavour physics. Among the earliest are measuring the production crosssections of beauty and charm hadrons and of the heavy-flavour quarkonium, $J/\psi$ and $\Upsilon$. These will provide a sensitive test bed of QCD predictions for production in proton-proton collisions at the LHC energies. While the main B-physics measurements will be taken with an instantaneous luminosity of around $10^{33} cm^{-2}s^{-1}$, the B-physics potential begins during the early data taking at lower luminosity of $10^{31} cm^{-2}s^{-1}$. With an integrated luminosity of $10 pb^{-1}$ ATLAS will already be able to register about $15·10^4$ events containing $J/\psi \to \mu^{+}\mu^{-}$ selected by the low luminosity trigger menu. Recorded events will contain $J/\psi (\mu\mu)$ produced both directly in proton proton interactions as well as indirectly from decays of B hadrons. With this statistics, beauty and quarkonia studies will play a key role in the early data-taking period. $J/\psi$ and its decay to di-muon final state will be utilized in calibration, alignment and determination of the trigger efficiencies. The availability of large sample of $J/\psi$ decay to muon pairs for these studies, especially at initial low luminosity, will depend strongly on reaching the lowest pT threshold and obtaining good understanding of the trigger performance and the tracking system. In this thesis we present a study of the ATLAS reach for the analysis of t he $J/\psi$ production in proton proton interaction at 14 TeV. The study focuses on the decays of the charmonium to muon pair. We discuss methods of separating promptly produced $J/\psi$ mesons from various background sources and review the ATLAS accessible range in transverse momentum and pseudorapidity and its implication on the spin alignment of the vector states. The separation of potential quarkonia production mechanism suggested by the theories and the feasibility of observing radiative decays of $\chi c$ decays is discussed.