Abstract
We systematically calculate the mass spectrum of the higher excited fully-charmed tetraquark $cc\bar c\bar c$ states including the S-wave radial excitations and the P-wave states with a nonrelativistic quark model. The quark model is composed of a vector one-gluon-exchange (OGE) and a scalar linear confinement interaction with the parameters determined by the charmonium spectrum. In the calculation, we consider both the $3_c-\bar 3_c$ and the $6_c-\bar{6}_c$ color representations. For the $cc\bar c\bar c $ state, the $6_c-\bar 6_c$ component is located lower than the $\bar 3_c-3_c$ one because of the stronger attractive interactions between the diquark and antidiquark. We focus on two excited modes and their properties for the P-wave tetraquarks. The mass splitting for the $\rho$-mode excitations with different color configurations is large. The low-lying $6_c-\bar 6_c$ $\rho$-mode component helps to explain the small mass gap between the ground S-wave and the P-wave tetraquark states. The recently observed $X(6900)$ state may be the candidate of the first radially excited tetraquarks with $J^{PC}=0^{++}$ or $2^{++}$, or the $1^{+-}$ or $2^{-+}$ P-wave states based on the mass spectrum. Moreover, the lowest $T_c$ states with the exotic $J^{PC}$ quantum numbers $0^{--}$ and $1^{-+}$ may decay into the P-wave $\eta_c J/\psi$ and di-$J/\psi$ modes, respectively. The future experimental search of these $T_c$ states will enrich the hadronic spectrum.
Highlights
Since 2003, dozens of the exotic states named as XYZ states were discovered in the mass range of the heavy quarkonium in experiments
Amounts of them cannot be categorized as the conventional QQ (Q 1⁄4 b, c) mesons, and are candidates of the multiquark states QQqqbased on their quantum numbers and decay channels
Various interpretations have been proposed for their nature, including the hadronic molecule, the compact tetraquark, the hado-charmonium, and so on
Summary
Since 2003, dozens of the exotic states named as XYZ states were discovered in the mass range of the heavy quarkonium in experiments. The light-meson-exchange interaction between two charmonia is suppressed, while the heavy quarks could be bound through the short-range colored forces arising from the gluon-exchange interaction in QCD. They are more likely to be candidates of the compact tetraquark states instead of the molecules. The most popular interpretations are the compact tetraquark states [39,40,41,42,43,44,45,46,47,48,49,50] Other rare interpretations, such as coupledchannel effects of double-charmonium channels [51,52], cchybrid [53], a Higgs-like boson [54] and so on, are proposed. In the Appendix, we give the spin, spin-orbital and tensor factors used in the calculation
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