Spectroscopy of the All-Charm Tetraquark

TL;DR

This paper models the mass spectrum of the all-charm tetraquark using a non-relativistic potential approach, providing predictions for its states and their stability, relevant for upcoming collider experiments.

Contribution

It introduces a diquark-antidiquark model with spin-dependent interactions to predict the spectrum of the all-charm tetraquark, aligning with experimental data.

Findings

Lowest S-wave tetraquarks may be below dissociation thresholds

Spin-dependent interactions are significant despite heavy quark masses

Orbital and radial excitations likely above charmonium thresholds

Abstract

We use a non-relativistic model to study the mass spectroscopy of a tetraquark composed by $c \, \bar{c} \, c \, \bar{c}$ quarks in the diquark-antidiquark picture. 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 of the heavy diquark mass, and that the diquark has a finite size if treated in analogy to 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 threshold. These states could be investigated in the forthcoming experiments at LHCb and Belle II.