Abstract
We use a non-relativistic model to study the spectroscopy of a tetraquark composed of in a diquark-antidiquark configuration. By numerically solving the Schrödinger 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 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 systems. We find that the lowest S-wave T4c 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 T4c states could be investigated in the forthcoming experiments at the LHC and Belle II.
Highlights
The existence of multiquark states with four or more quarks was proposed decades ago [1, 2]
In this work we first updated the Cornell model, obtaining a satisfactory reproduction of the charmonium spectrum, including the most recently measured states. We extended this model to study the all-charm tetraquark
We explored a diquark-antidiquark configuration, including P -wave tetraquarks, and we extended the spindependent interactions between diquarks, including a consistent strategy to deal with the tensor interaction between two objects of spin 1
Summary
The existence of multiquark states with four or more quarks was proposed decades ago [1, 2]. Most of the predictions for the T4c mass lead to values around 6 GeV, and lie well above the experimentally known range for charmonium (which is concentrated within 3 - 4.5 GeV) This energy gap makes the all-charm tetraquark a special object in the sector of exotic multiquarks. The absence of light quarks in the T4c makes it unlikely to be a meson-meson molecule, since it is not easy to describe this binding in terms of pion exchange or light vector meson exchange If it exists, the T4c is bound by QCD forces and studying its spectrum will lead to a more complete understanding of QCD interactions. Fig. 1. (color online) Pictorial representation of the all-charm tetraquark in the diquark-antiquark scheme
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