# A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark

## TL;DR

This paper develops a non-relativistic model to study the spectroscopy of the $[cc][ar{c}ar{c}]$ tetraquark, providing insights into its structure, spectrum, and potential experimental signatures.

## Contribution

It introduces a diquark-antidiquark model with spin-dependent interactions and solves the Schrödinger equation to describe the tetraquark spectrum, including effects of confinement and potential relevance to quark-gluon plasma.

## Key findings

- Lowest S-wave $T_{4c}$ tetraquarks may be below dissociation thresholds.
- Spin-dependent interactions are significant despite heavy diquark mass.
- Bound tetraquarks can exist even without the confining potential.

## Abstract

We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schr\"{o}dinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite the heavy diquark mass, and also that the diquark has a finite size if treated in the same way as the $c\bar{c}$ systems. We find that the lowest $S$-wave $T_{4c}$ tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds. Finally, we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks. This might be relevant to the study of exotic charmonium in the quark-gluon plasma. The $T_{4c}$ states could be investigated in the forthcoming experiments at the LHC and Belle II.