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

TL;DR

This paper calculates the mass spectra and wave functions of fully heavy tetraquarks using a Bethe-Salpeter approach, providing insights into their structure and possible experimental states.

Contribution

It introduces a relativistic Bethe-Salpeter framework to study fully heavy tetraquarks, including wave functions with mixing effects, and discusses implications for observed states like X(6900).

Findings

Ground states of ccar car c are around 6.4-6.5 GeV.

Ground states of bbar bar b are around 19.2-19.3 GeV.

X(6900) is likely an excited state, not the ground state.

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 $6.4\sim6.5$GeV, and the $bb\bar b\bar b$ states in mass range of $19.2\sim19.3$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.