An interpretation of the fully-charmed scalar state $X(6200)$ as a molecular di-meson

The LHCb Collaboration recently observed new structures in the invariant mass spectrum of $J/\psi J/\psi$ meson pairs produced in proton-proton collisions, including a narrow peak around $6.2$ GeV. This study investigates the thermal behavior of this newly discovered fully-charm resonance, assuming it to be an $\eta_c\eta_c$ molecule with quantum numbers $J^{PC} = 0^{++}$. Employing thermal QCD sum rules up to dimension four, we analyze the temperature dependence of the mass and the decay constant. Our results indicate that both physical quantities decrease as the temperature rises. Notably, at zero temperature, the mass and decay constant of the state are consistent with those reported in the existing literature. These findings are expected to provide valuable insights for future experimental investigations in this field.