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

TL;DR

This paper uses thermal QCD sum rules to study how the mass and coupling of the $X(3872)$ meson change with temperature, revealing stability up to 110 MeV and significant reduction near deconfinement.

Contribution

It provides the first thermal analysis of the $X(3872)$ meson using QCD sum rules with non-perturbative condensates up to six dimensions.

Findings

Mass and coupling constant are stable up to 110 MeV.

Mass and coupling decrease significantly after 110 MeV.

At deconfinement temperature, coupling reduces to about 34% of vacuum value.

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.