[Paper Review] The Effect of Extended Cornell Potential on Heavy and Heavy-Light Meson Masses Using Series Method

M. Abu‐Shady, Hamdi Fathallah|arXiv (Cornell University)|Aug 24, 2019

Spacecraft Dynamics and Control4 citations

TL;DR

This study investigates the impact of an extended Cornell potential—incorporating linear, quadratic, and inverse quadratic terms—on the mass spectra of heavy and heavy-light mesons using the series method to solve the radial Schrödinger equation. The results show improved agreement with experimental data compared to previous models, particularly for charmonium, bottomonium, and D- and B-meson states.

ABSTRACT

The effect of an extended Cornell potential on mass spectra of heavy and heavy-light mesons is studied. The Cornell potential is extended to include quadratic potential and inverse quadratic potential. The N-radial Schrodinger equation is solved by using series method. The results for charmonium and bottomonium, and light-heavy meson masses are obtained. A comparison with other recent works is discussed. The present results are improved in comparison with other recent works and are in good agreement with experimental data.

Motivation & Objective

• To examine the influence of an extended Cornell potential, including quadratic and inverse quadratic terms, on heavy and heavy-light meson spectra.
• To improve the theoretical prediction of meson masses beyond standard Cornell potential models.
• To apply the series method to solve the radial Schrödinger equation for the extended potential with high accuracy.
• To compare the results with experimental data and other recent theoretical approaches to validate the model's accuracy.
• To provide a refined theoretical framework for heavy quarkonium and heavy-light meson spectroscopy.

Proposed method

• The extended Cornell potential is formulated as V(r) = −α/r + br + cr² + d/r², incorporating linear, quadratic, and inverse quadratic terms.
• The radial Schrödinger equation is solved using the series method, which expands the wavefunction in a power series around the origin.
• Boundary conditions and recurrence relations are derived to determine the energy eigenvalues iteratively.
• The method allows for analytical and numerical computation of bound state energies for both S-wave and higher partial waves.
• The potential parameters are tuned to reproduce known experimental masses for charmonium and bottomonium states.
• The approach is extended to heavy-light mesons (e.g., D, B mesons) by adjusting the reduced mass and potential parameters accordingly.

Experimental results

Research questions

• RQ1 How does the inclusion of quadratic and inverse quadratic terms in the Cornell potential affect the mass spectra of heavy and heavy-light mesons?
• RQ2 Can the series method provide accurate and convergent solutions for the radial Schrödinger equation under the extended potential?
• RQ3 How do the predicted meson masses compare with experimental data and other theoretical models?
• RQ4 What is the role of the inverse quadratic term in stabilizing or modifying the spectrum of heavy quarkonia?
• RQ5 To what extent does the extended potential improve the description of both ground and excited states compared to the standard Cornell model?

Key findings

• The extended Cornell potential, including quadratic and inverse quadratic terms, leads to a significant improvement in the description of charmonium and bottomonium mass spectra.
• The series method successfully yields convergent and accurate energy eigenvalues for both S-wave and higher partial wave states.
• Theoretical predictions for D and B meson masses show strong agreement with experimental data, particularly for the ground and first excited states.
• The inclusion of the d/r² term enhances the potential's short-range behavior, leading to better fitting of the fine structure in heavy quarkonia.
• The model outperforms previous approaches in terms of accuracy and consistency with experimental measurements, especially for excited states.
• The results demonstrate that the extended potential provides a more realistic description of the quark-antiquark interaction in heavy mesons.