A non-relativistic model for the tetraquark**The authors acknowledge the support received from the brazilian funding agencies FAPESP (contract 12/50984-4), CNPq and CAPES. V. R. Debastiani also acknowledges the support from Generalitat Valenciana in the Program Santiago Grisolia (Exp. GRISOLIA/2015/005)

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.