Thermal properties of the exotic $X(3872)$ state via QCD sum rule

Abstract

In this work we investigate the $X(3872)$ meson with quantum numbers $J^{PC}=1^{++}$ in the framework of the thermal QCD sum rules method. We use a diquark-antidiquark current with the corresponding quantum numbers and calculate the two-point correlation function including contributions of non-perturbative condensates up to six dimensions. Analysis of the obtained thermal sum rule allows us to study contributions of a medium to the mass and coupling constant of the $X(3872)$ resonance. Our numerical calculations demonstrate that the mass and the meson-current coupling constant are insensitive to the variation of temperature up to $T=110\sim MeV$ , however after this point; they start to fall by increasing the temperature. At deconfinement temperature, the meson-current coupling constants attain roughly to $34\%$ of the vacuum value.