Approximate Bound State Solutions of the Fractional Schr\"odinger Equation under the Spin-Spin-Dependent Cornell Potential

TL;DR

This paper derives approximate solutions for the fractional Schrödinger equation with a spin-dependent Cornell potential, improving heavy meson mass predictions and aligning well with experimental data.

Contribution

It introduces a novel application of the fractional Schrödinger equation with a spin-dependent Cornell potential to compute heavy meson spectra, enhancing accuracy over existing models.

Findings

Mass spectra align closely with experimental data.

Fractional parameters improve the accuracy of meson mass predictions.

Potential curves with fractional parameters model quark interactions effectively.

Abstract

In this work, the approximate bound state solutions of the fractional Schr\"odinger equation under a spin-spin-dependent Cornell potential are obtained via the convectional Nikiforov-Uvarov approach. The energy spectra are applied to obtain the mass spectra of the heavy mesons such as bottomonium, charmonium and bottom-charm. The masses for the singlet and triplet spin numbers increase as the quantum numbers increase. The fractional Schr\"odinger equation improves the mass spectra compared to the masses obtained in the existing literature. The bottomonium masses agree with the experimental data of the Particle Data Group where percentage errors for fractional parameters of \b{eta}=1,{\alpha}=0.97 and \b{eta}=1,{\alpha}=0.50 were found to be 0.67% and 0.49% respectively. The respective percentage errors of 1.97% and 1.62% for fractional parameters of \b{eta}=1,{\alpha}=0.97 and \b{eta}=1,{\alpha}=0.50 were obtained for charmonium meson. The results indicate that the potential curves coupled with the fractional parameters account for the short-range gluon exchange between the quark-antiquark interactions and the linear confinement phenomena which is associated with the quantum chromo-dynamic and phenomenological potential models in particle and high-energy physics