# Spectrum of the fully-heavy tetraquark state $QQ\bar Q' \bar Q'$

## TL;DR

This paper calculates the mass spectra of fully heavy tetraquark states using two nonrelativistic quark models, revealing their possible configurations and the likelihood of bound states.

## Contribution

It provides a systematic analysis of the mass spectra and configuration mixing of fully heavy tetraquarks within two quark models, including effects of hyperfine interactions and coupled channels.

## Key findings

- $6_c-ar 6_c$ configuration is lower for $J^{PC}=0^{++}$ states in both models.
- Ground states are above scattering thresholds, suggesting no bound states.
- Mixing effects are mainly due to hyperfine interactions, with Coulomb and confinement contributions vanishing.

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