Spectroscopy of the tetraquark $c\bar{c}$-$c\bar{c}$ in a non-relativistic approach using a phenomenological QCD model

Abstract

Hadron spectroscopy is a powerful tool for testing the standard model and for the search of new physics. In this work, we create a tetraquark model from a di-meson interaction inspired by Jacobi coordinates. We consider mesons as thick points and quantify their interaction with the quark-antiquark interaction through a factor k (that takes approximately the value 2) in a central phenomenological potential, reducing the four-body problem finally to a one body equivalent problem. The eigenproblem is solved using a combination of the DVR method and perturbation theory in a C++ code. We obtain a mass spectrum for the tetraquark between 6 GeV and 8 GeV for the ground and first energy excitation level. Our calculation indicates that our system is compact and that the non-relativistic approach used in all our formalism is valid.