Spectroscopic Properties of the Molecular $T_{cc}^{+}$ Meson in a Thermal Medium

In this work, we investigate the exotic doubly charmed molecular state $T_{cc}^{+}(3875)$ with quantum numbers $J^{P} = 1^{+}$ using the Thermal QCD Sum Rules framework. Employing a molecular interpolating current, we evaluate the two-point correlation function by incorporating non-perturbative condensate contributions up to dimension six. From the resulting thermal sum rules, we determine the temperature dependence of the mass, decay constant, and width of the $T_{cc}^{+}$ state. Our numerical analysis reveals that all quantities remain remarkably stable under temperature variations up to $T \simeq 120~\text{MeV}$, after which they change significantly. At the deconfinement temperature, the mass decreases to approximately $28\%$ of its vacuum value, and the decay constant drops to about $25\%$. We analyze the thermal evolution of the decay width of $T_{cc}^{+}$, finding $\Gamma_{T_{cc}^{+}}(0) = 434.95 \pm 7.66~\text{keV}$ at zero temperature. The width of $T_{cc}^{+}$ remains unchanged until $T\simeq 120~\text{MeV}$, after which it begins to grow rapidly. The investigation of thermal effects on $T_{cc}^{+}$ provides new insights into QCD phase transitions, chiral symmetry restoration, and the properties of strongly interacting, hot, and dense matter. These findings are expected to serve as useful input for future experimental searches and phenomenological studies of exotic mesons.