Upsilon (1S) polarization measurement in PbPb collisions at $\sqrt{^sNN} = 5.02 TeV$ using the CMS detector

The study of quarkonium polarization in heavy ion collisions provides crucial information about the quark-gluon plasma (QGP), a deconfined state of matter formed at extreme temperature and Energy density. In heavy ion collisions, the polarization of quarkonium states can be sensitive to extreme conditions in the QGP, such as strong electromagnetic and rotational fields, and may reflect screening effects and the degree of thermalization in the QGP. While quarkonium suppression in heavy ion collisions has been extensively studied as a QGP signature, measurements of quarkonium polarization remain relatively limited due to experimental challenges. This thesis presents a measurement of the polarization of $\varUpsilon$ mesons in lead-lead (Pb+Pb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}$ = 5.02 TeV, using data collected by the Compact Muon Solenoid (CMS) experiment during the 2018 heavy ion run at the Large Hadron Collider (LHC). The analysis is performed in the dimuon decay channel as a function of transverse momentum ($p_T$) within the midrapidity region ($|y| < 2.4$). Polarization parameters ($\lambda_\theta$, $\lambda_\varphi$, and $\lambda_{\theta\varphi}$) are extracted from the angular distributions of the decay muons in the Collins-Soper (CS) and helicity (HX) frames. Acceptance and efficiency corrections are derived using fully simulated Monte Carlo (MC) samples, with generator-level and reconstructed-level corrections applied to the angular distributions. A frame-invariant parameter, $\tilde{\lambda}$, is also evaluated in order to facilitate a frame-independent interpretation. The results are compared to corresponding measurements in proton-proton (p+p) collisions to assess possible modifications due to QGP effects. This work provides new experimental input for theoretical models of quarkonium production and polarization in a QGP medium.