Abstract
We study the properties of fully-heavy tetraquarks at finite temperature and their production in high-energy nuclear collisions. We obtain the masses and wave functions of the exotic hadron states $cc\bar c\bar c$ and $bb\bar b\bar b$ by solving the four-body Schr\"odinger equation in vacuum and strongly interacting matter. In vacuum, the tetraquarks are above the corresponding meson-meson mass threshold, and the newly observed exotic state $X(6900)$ might be a $cc\bar c\bar c$ state with quantum number $J^{PC}=0^{++}$ or $1^{+-}$. In hot medium, the temperature dependence of the tetraquark masses and the dissociation temperatures are calculated. Taking the wave function at finite temperature, we construct the Wigner function for the tetraquark states and calculate, with coalescence mechanism, the production yield and transverse momentum distribution of $cc\bar c\bar c$ in heavy-ion collisions at LHC energy. In comparison with nucleon-nucleon collisions, the yield per binary collision is significantly enhanced.
Highlights
The quantum chromodynamics (QCD), which is widely accepted as the theory of strong interaction, allows the existence of exotic hadrons, such as glueballs containing only gluons [1,2], hybrids with quarks and gluons [3,4], multi-quark states like tetraquarks and pentaquarks [5,6] and hadronic molecules [7,8]
We found that the masses of all the tetraquark states 1S; 2S and 3S with JPC 1⁄4 0þþ; 1þ− and 2þþ are above the 2mJ=ψ or 2mΥ threshold
The experimentally observed exotic state Xð6900Þ is likely to be a tetraquark state of cccc, and the possible quantum number is JPC 1⁄4 0þþ or 1þ−
Summary
The quantum chromodynamics (QCD), which is widely accepted as the theory of strong interaction, allows the existence of exotic hadrons, such as glueballs containing only gluons [1,2], hybrids with quarks and gluons [3,4], multi-quark states like tetraquarks and pentaquarks [5,6] and hadronic molecules [7,8]. If neglecting the interaction between colorsinglet and color-octet states, the pNRQCD becomes a potential model [41] In this case, one can employ the Schrödinger equation to study the properties of hadrons consist of only heavy quarks. We employ the four-body Schrödinger equation to study the properties of fully-heavy tetraquark states ccccand bbbbat finite temperature and their production in high-energy nuclear collisions. Different from light hadrons where the coalescence probability is assumed to be a Gaussian distribution, the probability for fully-heavy tetraquarks is derived from the wave function of the system controlled by the Schrödinger equation This is essential for predicting the properties of unconfirmed particles. VI, we provide supplementary informations about the hyperspherical harmonic functions in Appendix A, and the method to compute the potentials is described in Appendix B
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