Mass spectra and wave functions of $T_{QQ\bar{Q}\bar{Q}}$ tetraquarks

Abstract

The compact tetraquark states with fully heavy quark contents $QQ\bar{Q}\bar{Q}$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$. Our results show that the three ground states of $cc\bar{c}\bar{c}$ locate in the mass range of $6.4\sim 6.5$GeV, and the $bb\bar{b}\bar{b}$ states in mass range of $19.2\sim 19.3$GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$\,(or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCb's observation $X(6900)$ is less likely to be the ground states of compact $cc\bar{c}\bar{c}$ tetraquarks but might be the first or second excited states. In addition, a widely used propagator-like form factor is also investigated and discussed.

Comments: 18 pages, 23 figures, Version updated with the PRD