Mass spectra and wave functions of TQQQ¯Q¯ tetraquarks

Abstract

The compact tetraquark states with fully heavy quark contents $QQ\overline{Q}\overline{Q}$ 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 ${J}^{PC}={0}^{++}$, ${1}^{+\ensuremath{-}}$, and ${2}^{++}$. Our results show that the three ground states of $cc\overline{c}\overline{c}$ locate in the mass range of 6.4--6.5 GeV, and the $bb\overline{b}\overline{b}$ states in mass range of 19.2--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 $cc\overline{c}\overline{c}$ tetraquarks but might be the first or second excited states. In addition, a widely used propagatorlike form factor is also investigated and discussed.