Fully-heavy tetraquarks in the vacuum and in a hot environment

Abstract

We study the thermal behavior of quarkonia and fully-heavy tetraquark states associated to the charmonium, bottomonium and bottom-charmonium mass spectra. The starting point is the Schr\"odinger formalism with a vacuum Cornell-like potential. The spin-spin, spin-orbit and tensor contributions are also considered to describe the structure of the vacuum quarkonia $Q\bar Q$ spectra ($Q$ denoting $c,b$ quarks). The parameters of the model are fixed using the experimental data of the $Q\bar Q$ states. After that, this formalism is extended to the fully-heavy tetraquark states within the $1^3 S_1$ axial diquark--$1^3 S_1$ axial antidiquark configuration $[QQ] [\bar Q \bar Q]$, and their vacuum mass spectra are obtained and compared to the experimental data recently obtained. Our predictions support the interpretation of the $X(6600)$ (or $X(6552)$), $X(6900)$ and $X(7200)$ states as the radially-excited $T_{4c}(n^1S_0)$ configurations with $n=2,3,4$. In the sequence, we evaluate the mass spectra behavior in a thermal medium, by introducing a modified temperature-dependent Cornell potential. As a consequence, this formalism enables us to get some insight into the dissociation mechanism of $[QQ] [\bar Q \bar Q]$ states caused by a thermal medium, and into the temperature range at which the tetraquark states might be formed. We find that these structures cannot be formed in the thermal medium when the system has a temperature higher than about twice the critical temperature. These findings may be useful to better understand the features of the exotics in heavy-ion collisions. [NOTE: version with inclusion of an Addendum incorporating the $2^{++}$ state predictions, motivated by the new CMS results [arXiv:2506.07944].]