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

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 Schrödinger 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.

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• Thermodynamic properties of the trigonometric Rosen-Morse potential and applications to a quantum gas of mesons
• Hard confinement of a two-particle quantum system using the variational method
• Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement
• Saturation effect in confined quantum systems with energy-dependent potentials