Higher fully-charmed tetraquarks: Radial excitations and P-wave states

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.

Comments: 15 pages, 3 figures. Version published in PRD