Abstract
In this work, we systematically calculate the mass spectra of the $S$-wave fully heavy tetraquark states $bb\bar b\bar b$, $cc\bar c\bar c$, and $bb\bar c\bar c$ in two nonrelativistic quark models. A tetraquark state may be an admixture of a $6_c-\bar 6_c$ state and a $\bar 3_c-3_c$ one, where $6_c-\bar 6_c$($\bar 3_c-3_c$) denotes the color configuration with a $6_c$ ($\bar 3_c$) diquark and a $\bar 6_c$ ($3_c$) antidiquark. For the tetraquark states $bb\bar b\bar b$ and $cc\bar c\bar c$ with $J^{PC}={0^{++}}$, the $6_c-\bar 6_c$ state is lower than the $\bar 3_c-3_c$ one in both the two quark models, while the order of the $bb\bar c\bar c$ states depend on models. The $6_c-\bar 6_c$ and $\bar 3_c-3_c$ mixing effects are induced by the hyperfine interactions between the diquark and antidiquark, while the contributions from the one-gluon-exchange (OGE) Coulomb or the linear confinement potentials vanish for the $QQ\bar Q'\bar Q'$ system. With the couple-channel effects, we obtain the similar mass spectra. The numerical results show that the ground $QQ\bar Q'\bar Q'$ ($Q=b,c$ and $Q'=b,c$) tetraquark states are located above the corresponding scattering states, which indicates that there may not exist a bound state in the scheme of the two quark models.
Highlights
Since 2003, numerous exotic structures have been observed in experiments [1,2,3,4,5,6,7,8,9,10,11], amongst which many states cannot be accommodated into the traditional quark model
The 6c − 6 ̄c and 3 ̄c − 3c mixing effects are induced by the hyperfine interactions between the diquark and antidiquark, while the contributions from the one-gluon-exchange Coulomb or the linear confinement potentials vanish for the QQQ 0Q 0 system
The numerical results show that the ground QQQ 0Q 0 (Q 1⁄4 b, c and Q0 1⁄4 b, c) tetraquark states are located above the corresponding scattering states, which indicates that there may not exist a bound state in the scheme of the two quark models
Summary
Since 2003, numerous exotic structures have been observed in experiments [1,2,3,4,5,6,7,8,9,10,11], amongst which many states cannot be accommodated into the traditional quark model. The fully-heavy tetraquark state is a golden system to investigate the inner color configuration of the multiquark states. Since 1975, there have been many theoretical works about the mass spectroscopy of the fully-heavy quark states [26,27,28,29,30,31,32]. To investigate the existence of the fully-heavy tetraquark states, we systematically calculate the mass spectra of the bbbb ̄ , cccc ̄ and bbcc ̄ðccbb ̄ Þ in two nonrelativistic quark models. With the couple-channel effects, we perform the dynamical calculation of the mass spectra of the tetraquark states and investigate the inner structures of the ground states. IV, we compare our results with those in other models and give a brief summary
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