Spectrum of the fully-heavy tetraquark state $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$

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 $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$ system. With the couple-channel effects, we obtain the similar mass spectra. The numerical results show that the ground $QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }$ ($Q=b,c$ and $Q^{\prime }=b,c$) 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.

13 pages, 6 figures