Investigating the medium effects on full charmonium meson molecules

The experimental observation of exotic hadrons has made significant contributions to both theoretical and experimental studies in high-energy physics. These particles provide valuable insights into the dynamics of quarks and gluons, the nature of strong interactions, and the development of new experimental methods. Although these exotic particles have been observed experimentally, their structures, formation dynamics, and interactions with their environment are not yet fully understood. In 2020, in the double J/ψ production spectrum observed in proton-proton collisions by the LHCb Collaboration, a full charmonium resonance was detected around 6.2 GeV. This resonance was named 𝑇𝑇𝑐𝑐𝑐𝑐¯𝑐𝑐𝑐𝑐¯(6200)0. In this thesis, the spectroscopic properties of the 𝑇𝑇𝑐𝑐𝑐𝑐¯𝑐𝑐𝑐𝑐¯(6200)0 resonance in a thermal medium were analyzed using the Thermal Quantum Chromodynamics Sum Rules method. The 𝑇𝑇𝑐𝑐𝑐𝑐¯𝑐𝑐𝑐𝑐¯(6200)0 resonance was modeled as an 𝜂𝜂𝑐𝑐𝜂𝜂𝑐𝑐 molecule with quantum numbers 𝐽𝐽𝑃𝑃𝑃𝑃 = 0++, and in the calculations, non-perturbative contributions up to dimension four were also taken into account. In this study, the results obtained for the mass and decay constant of the exotic state at low temperatures were found to be consistent with existing theoretical and experimental data in the literature. A more recent and accurate fit for the temperature threshold proposed for charmonium states was used in the calculations, and this fit was applied to QCD sum rules for the first time in this thesis. It was observed that as the temperature approached the critical point, where the transition to quark-gluon plasma begins, the mass of the charmonium molecule started to decrease, eventually dropping below the 2 𝜂𝜂𝑐𝑐𝜂𝜂𝑐𝑐 threshold. However, after crossing the critical temperature, the mass increased again, reaching the 2 𝜂𝜂𝑐𝑐𝜂𝜂𝑐𝑐 threshold around 200 MeV. Similar to the mass, the leptonic decay constant also decreased near the critical temperature, but unlike the mass, the decay constant did not increase with increasing temperature; instead, it remained stable at a value close to that of the 𝜂𝜂𝑐𝑐. These results suggest that the gluon exchange mechanism begins to relax near the critical temperature and breaks down completely beyond it, and also 𝜂𝜂𝑐𝑐𝜂𝜂𝑐𝑐 particles start to dissolve. Nonetheless, around 200 MeV, the charmonium states recover and regain their structural integrity. These findings align with the behavior proposed in the literature for heavy quarkonium states and have been theoretically demonstrated for the first time in this thesis.