Heavy quarkonia properties from a hard-wall confinement potential model with conformal symmetry perturbing effects

TL;DR

This paper models heavy quarkonia using a hard-wall potential with conformal symmetry considerations, deriving spectra and radii that align well with experimental data, highlighting the role of symmetry perturbations.

Contribution

It introduces a novel potential model incorporating conformal symmetry and its perturbation to study heavy quarkonia properties.

Findings

Predicted mass spectra closely match experimental data.

Small conformal symmetry perturbations improve model accuracy.

Wave functions and radii are obtained in closed form.

Abstract

Heavy $c\bar c$ and $b\bar b $ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent-- with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov-Uvarov method the associated radial Schr\"{o}dinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status of conformal symmetry in the heavy flavor sector. The resulting predictions on heavy quarkonia mass spectra and root mean square radii are compared with the available experimental data, as well as with predictions by other theoretical approaches. We observe that a relatively small conformal symmetry perturbing term in the potential suffices to achieve good agreement with data.