Search for the decay X(3872)$\to J/\psi \omega$ in the LHCb experiment at CERN

In the Standard Model of particles, any non [$q\bar{q}$] or [$qqq$] composite state is labelled as $\textit{exotic}$: this includes different combinations which are in principle allowed (tetraquark, pentaquark, mesonic molecule, glueball, and other) but were never observed for a long time, up to 2003 when the Belle Collaboration at KEK reported the observation of a narrow peak in the $J/\psi \pi^+ \pi^-$ invariant mass spectrum. The state, labelled as X(3872), must contain a $c\bar{c}$ pair but its mass does not correspond exactly to any of the predicted states in the charmonium excitation spectrum. Several theoretical models have been developed to describe the nature of the X(3872), such as mesonic molecule, tetraquark, threshold effect, hybrid $c\bar{c}g$ resonance, and others. After the Belle announcement, it was observed also by several others Collaborations (CDF, D0, BaBar, LHCb): BaBar observed evidence for the decay X(3872)$\to J/\psi \omega$ at a rate comparable to that of $J/\psi \pi\pi$, suggesting the presence of maximal isospin violation. The analysis of the first channel favoured the $J^{PC} = 2^{-+}$ hypothesis, while LHCb measured $J^{PC} = 1^{++}$ in the $J/\psi \pi\pi$ channel with 8.2$\sigma$ rejection of the $2^{-+}$ hypothesis. The maximal isospin violation could mean that the two aforementioned decay channels come from two different isospin eigenstates: it is therefore necessary to repeat the BaBar analysis in order to measure the X(3872) quantum numbers in the $J/\psi \omega$ channel. In this thesis, a search for X(3872)$\to (J/\psi \to \mu^+ \mu^-) (\omega \to \pi^+ \pi^- \pi^0)$ in the B$^+ \to K^+ J/\psi \omega$ decay channel is presented. The analysis has been performed with data collected by the LHCb detector at the Large Hadron Collider (LHC) at CERN during 2011 and 2012, corresponding to an integrated luminosity of 1 (2011) + 2 (2012) fb$^{-1}$ at an energy of centre of mass of, respectively, 7 and 8 TeV. The event reconstruction algorithm combines two pions with opposite charge, a charged kaon and a photon pair forming two separate clusters in the calorimeter with a $J/\psi \to \mu^+ \mu^-$ candidate, detached from the primary vertex, selected by a dedicated StrippingLine. The events are then processed through a multivariate classifier from which two different selections are extracted: the first one, tighter, is used to observe the decay B$^+ \to K^+ J/\psi \eta$ and estimate its branching fraction; the second one, looser, is used to observe an excess of events in the $J/\psi \omega$ mass spectrum over a phase space MC simulation in the kinematic threshold region, corresponding to the X(3872) and $\chi_{c0}(2$P) contributions. The sum of X(3872) and $\chi_{c0}$(2P) branching fractions, normalised to non resonant B$^+ \to K^+ J/\psi \omega$, is then computed, and is found to be consistent within 2$\sigma$ with existing publications. Due to lack of statistics in the region of interest it was not possible to perform an angular analysis and to measure the X(3872) quantum numbers in the decay channel object of this thesis: this measurement will be possible with the statistics accumulated from 2015 to 2018 with the LHC Run-II.