Mass spectra and wave functions of TQQ(Q)over-bar(Q)over-bar tetraquarks

The compact tetraquark states with fully heavy quark contents QQ (Q) over bar(Q) over bar 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 (c) over bar(c) over bar locate in the mass range of 6.4-6.5 GeV, and the bb (b) over bar(b) over bar 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 (c) over bar(c) over bar tetraquarks but might be the first or second excited states. In addition, a widely used propagatorlike form factor is also investigated and discussed.

Automated summary

This study investigates compact tetraquark states with fully heavy quark contents, deriving mass spectra and wave functions numerically. The results show the ground state mass ranges for cc (c) over bar(c) over bar and bb (b) over bar(b) over bar tetraquarks. The relativistic wave functions obtained can be used for precise calculations of tetraquark decays, suggesting that the observed X(6900) by LHCb may not be the ground state but possibly an excited state. Additionally, a widely used propagatorlike form factor is also explored and discussed.