QQ-onia package: a numerical solution to the Schrodinger radial equation for heavy quarkonium

TL;DR

The QQ-onia package provides a numerical solution to the Schrödinger radial equation for heavy quarkonium, enabling analysis of resonance properties, spin effects, and transition rates using the Numerov method.

Contribution

It introduces a comprehensive software package that implements the Numerov method for solving the Schrödinger equation in heavy quarkonium systems, including analysis tools for various physical properties.

Findings

Accurate computation of wave functions and derivatives at the origin.

Analysis of hyperfine splittings and energy levels.

Calculation of E1 transition rates.

Abstract

This paper presents the basics of the QQ-onia package, a software based upon the Numerov method which can be used to solve the Schrodinger radial equation using a suitable potential V(r) for the heavy quarkonium system. This package also allows the analysis of relevant properties of those resonances such as the wave functions at the origin, their corresponding derivatives for l \neq 0 states, typical heavy quark velocities, and mean square radii. Besides, it includes a tool to analize the spin-dependent contributions to the heavy quarkonia spectrum, providing the hyperfine splittings, as well as the nPJ energy levels. Finally, a simple software implemented in QQ-onia to compute E1 transition rates is presented.