J/$\Psi$-J/$\Psi$ scattering cross sections of Quadratic and Cornell Potentials

TL;DR

This paper investigates J/$\Psi$-J/$\Psi$ scattering cross sections in a tetraquark system using Quadratic and Cornell potentials, revealing that the Quadratic potential yields higher scattering cross sections than the Cornell potential.

Contribution

It introduces a method to compute scattering cross sections in a tetraquark system using adiabatic approximation and resonating group technique with two different potentials.

Findings

Quadratic potential results in higher scattering cross sections than Cornell potential.

The approach combines wavefunction analysis with integral equations to derive scattering properties.

Comparison of potentials provides insights into meson-meson interactions in tetraquark systems.

Abstract

We study the scattering of J/$\Psi$-J/$\Psi$ mesons using Quadratic and Cornell potentials in our tetraquark ($c$$\bar{c}$$c$$\bar{c}$) system. The system's wavefunction in the restricted gluonic basis is written by utilizing adiabatic approximation and Hamiltonian is used via quark potential model. Resonating group technique is used to get the integral equations which are solved to get the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions and eventually the scattering cross sections are obtained using the two potentials respectively. We compare these cross sections and find that the magnitude of scattering cross sections of Quadratic potential are higher than Cornell potential.