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 Schrödinger 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 $T_{4c}(n^1{S}_0)$ 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].]

arXiv commentVersion with the inclusion of an Addendum incorporating the $2^{++}$ state predictions, motivated by the new CMS results [arXiv:2506.07944]. 17 pages, 5 figures, 9 tables; published in EPJ C

References in corpus (46)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Higher Charmonia
• Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
• An updated review of the new hadron states
• Exotica
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Real-time static potential in hot QCD
• $J/\psi$ and ${\eta }_c$ in the Deconfined Plasma from Lattice QCD
• Observation of structure in the $J/\psi$-pair mass spectrum
• Heavy-quark symmetry implies stable heavy tetraquark mesons $Q_i{Q}_j{\bar{q}}_k{\bar{q}}_l$
• Heavy Quarkonium in Extreme Conditions
• A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark
• Spectrum of fully-heavy tetraquarks from a diquark+antidiquark perspective
• Masses of fully heavy tetraquarks $QQ\bar{Q}\bar{Q}$ in an extended relativized quark model
• New structures in the J/$\psi$J/$\psi$ mass spectrum in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Observation of an excess of di-charmonium events in the four-muon final state with the ATLAS detector
• The Simple Spectrum of $c\bar{c}c\bar{c}$ States in the Dynamical Diquark Model
• A study of $cc\bar{c}\bar{c}$ tetraquark decays in 4 muons and in $D^{(\ast )}{\bar{D}}^{(\ast )}$ at LHC
• Systematics of fully heavy tetraquarks
• Masses of the $QQ\bar{Q}\bar{Q}$ tetraquarks in the relativistic diquark--antidiquark picture
• Strong decays of fully-charm tetraquarks into di-charmonia
• Interpretation of structure in the di-$J/\psi$ spectrum
• Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity
• Search for $bb\bar{b}\bar{b}$ tetraquark decays in 4 muons, $B^{+}{B}^{-}$, $B^0{\bar{B}}^0$ and $B_s^0{\bar{B}}_s^0$ channels at LHC
• Doubly Charmed Tetraquarks in B_c and Xi_bc Decays
• The excited bottom-charmed mesons in a nonrelativistic quark model
• Nonrelativistic Treatment of Fully-Heavy Tetraquarks as Diquark-Antidiquark States
• $0^{+}$ fully-charmed tetraquark states
• Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data
• Quarkonium in-medium properties from realistic lattice NRQCD
• The possible tetraquark states $cc\bar{c}\bar{c}$ observed by the LHCb experiment
• Tetraquark Production in Double Parton Scattering
• Some remarks on $X(6900)$
• Fully-heavy tetraquark production by $\gamma \gamma$ interactions in hadronic collisions at the LHC
• Exploring fully heavy scalar tetraquarks $QQ\overline{Q}\overline{Q}$
• Multiplicity of the doubly charmed state $T_{cc}^{+}$ in heavy-ion collisions
• Benchmark calculations of fully heavy compact and molecular tetraquark states
• Analysis of the $X(6600)$, $X(6900)$, $X(7300)$ and related tetraquark states with the QCD sum rules
• Spectrum of $cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}$, and $bc\bar{b}\bar{b}$ Tetraquark States in the Dynamical Diquark Model
• Interactions of the doubly charmed state $T_{cc}^{+}$ with a hadronic medium
• NLO results with operator mixing for fully heavy tetraquarks in QCD sum rules
• Fully-heavy structures in the invariant mass spectrum of $J/\psi \psi (3686)$, $J/\psi \psi (3770)$, $\psi (3686)\psi (3686)$, and $J/\psi {\rm Y}(1S)$ at hadron colliders
• The two-photon decay of X(6900) from light-by-light scattering at the LHC
• Towards a precision determination of the $X(6200)$ parameters from data
• A potential approach to the $X(3872)$ thermal behavior
• $J/\psi$ near $T_c$