Observation and study of the X(3872) particle with the CMS experiment at LHC

The discovery of the $X(3872)$ resonance in the decay channel $J/\psi \pi^+ \pi^-$ by Belle Collaboration in $2003$ opened up a new chapter in the QCD landscape. Its subsequent observation in other experiments confirms the existence of this new particle. \\The properties of $X(3872)$ are not in agreement with being a charmonium state. Different interpretations are still under study. One possible option is that it is a molecule of $D^{*}$ mesons, another one is that it is a hybrid of bound state and a tetra-quarks state. \\In this thesis it will be reported the study of the $X(3872)$ particle in the CMS experiment, at LHC, in the $2010$ and a first view at the $2011$ data. The observed decay channel is that one into a $J/\psi$ (reconstructed with a muons pair) and a pions pair ($\pi^+ \pi^-$). \\The CMS experiment, one of the two general purpose experiments in the LHC collider, has an impressive performance in the tracks and muons detection and reconstruction, due to the superior tracking performances. This allows the detection of high purity signal for the $J/\psi$ mesons and to reconstruct the $X(3872)$ particle. \\In this thesis it will be shown the measurement procedure of the production cross section ratio of the $X(3872)$ and $\psi(2S)$ in the same decay channel, using the statistics collected by CMS at $\sqrt{s}=7\,TeV$ at LHC in $2010$, corresponding to $\sim 40\,pb^{-1}$ of integrated luminosity. The measurement of the ratio is convenient because of the cancellation of the errors, such the one of the luminosity and the one of the trigger. The value of the ratio is: $R= 0.084\,\pm0.017(stat.)\,\pm0.009(syst.)$. \\The increased number of reconstructed $X(3872)$, $5310\pm342$, in the $2011$ collisions permits to continue the study of this particle. More study is undergoing, in this thesis it will be also shown a preliminary look at the first part of the $2011$ data and a study of the non-prompt composition of the $X(3872)$ in the data.