Abstract
We calculate the masses of the $qq\overline{q}\overline{q}$ tetraquark ground state and first radial excited state in a constituent quark model where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. The three coupling parameters for the Cornell-like potential and one-gluon exchange spin-spin coupling are proposed mass-dependent in accordance with lattice QCD data, and all model parameters are predetermined by studying light, charmed, and bottom mesons. The theoretical predictions for light tetraquarks are compared with the observed exotic meson states in the light-unflavored meson sector, and tentative assignments are suggested. The work suggests that ${f}_{0}(1500)$ and ${f}_{0}(1710)$ might be ground light tetraquark states with $J=0$.
Highlights
Low-lying baryons and mesons, even for the light quark sector, can be reasonably described in nonrelativistic quark models (NQM), where the interaction of constituent quarks is interpreted in terms of potentials which are usually phenomenologically motivated [1]
Some resonances around 1370 MeV observed in the KKchannel might be good candidates for the 13P0 ssstate [6]. Since both the f0ð1500Þ and f0ð2020Þ were observed by E835 in the process pp → ðηηÞπ [16], we may group the f0ð1500Þ and f0ð2020Þ to be the ground states and first radial excited states respectively, with J 1⁄4 0, of the jψ c3 ̄⊗3ψ ðS01⁄4⊗00Þ,ψ c6⊗6 ̄ ψ ðS11⁄4⊗01Þi mixed configuration. Considering that both the f0ð1710Þ and f0ð2100Þ were observed by BESIII in the process J=ψ → γðηηÞ [18], and the f0ð2020Þ was observed by E835 in the process pp → ðηηÞπ and their decay widths are in the same order [16], and both the f0ð1710Þ and f0ð2200Þ were observed by BES in the process ψð2sÞ → γπþπ−ðKþK−Þ with the same order decay widths [17], we may assign the f0ð1710Þ and f0ð2020Þ to be the ground states, the f0ð2100Þ and f0ð2200Þ to be the first radial excited state with J 1⁄4 0 of the jψ c3 ̄⊗3ψ ðS11⁄4⊗01Þ,ψ c6⊗6 ̄ ψ ðS01⁄4⊗00Þi mixed configuration, respectively
The masses of ground and first radial excited light tetraquark states have been evaluated, with all model parameters predetermined by fitting the masses of light, 036001-5
Summary
Low-lying baryons and mesons, even for the light quark sector (with the exception of the would-be Goldstone bosons of the chiral symmetry breaking, first the pions), can be reasonably described in nonrelativistic quark models (NQM), where the interaction of constituent quarks is interpreted in terms of potentials which are usually phenomenologically motivated [1]. (n > 1) and orbital excitations (L > 0) are still missing and some observed meson candidates do not fit into quark model conventional meson mass spectra [8]. The research on conventional qqstates conducted for more than a half century provide us with a good knowledge to understand their underlying structures Exotic meson states such as glueballs, hybrids, and tetraquarks have been widely studied in the past two decades, especially focusing on the states having same quantum numbers as conventional qqsystems.
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