Potential model prediction of fully-heavy tetraquarks $QQ\bar{Q}\bar{Q}$ ($Q=c, b$)

TL;DR

This study uses a nonrelativistic potential model and advanced computational methods to investigate fully-heavy tetraquarks, predicting narrow resonances in charm and bottom systems that align with recent experimental observations.

Contribution

The paper introduces a comprehensive four-body calculation approach for fully-heavy tetraquarks, incorporating various configurations and employing the complex scaling method to identify resonances.

Findings

No S-wave bound states found in fully-charm or fully-bottom systems.

Several narrow resonances predicted in both charm and bottom tetraquarks.

Resonance structures in the charm sector match recent LHCb observations.

Abstract

The fully-heavy tetraquark states $QQ\bar{Q}\bar{Q}$ ($Q=c, b$) are systematically investigated by means of a nonrelativistic potential model. The model is based on the lattice QCD study of the two-body $Q\bar{Q}$ interaction, which exhibits a spin-independent Cornell potential along with a spin-spin interaction. The four-body problem is implemented with a highly accurate computational approach, the Gaussian expansion method. The complex scaling method is also employed so that the bound, resonance, and scattering states can be treated on the same footing. Complete set of the four-body configurations, including meson-meson, diquark-antidiquark, and K-type configurations, as well as their couplings, are considered for spin-parity quantum numbers $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$ in the $S$-wave channel. No $S$-wave bound state is found either in the fully-charm tetraquark system or in the fully-bottom one. However, several narrow resonances, with widths less than 10 MeV in two-meson strong decay, are found in both of these two systems. For the fully-charm case, the recently reported resonance structures between 6.2 and 7.2 GeV in the di-$J/\psi$ invariant spectrum by the LHCb collaboration, can be well identified in our calculation. For the fully-bottom case, resonances with masses between 18.9 and 19.6 GeV are found. The predicted resonances can be further examined in future experiments.