Mass Spectrum of Heavy Mesons using WKB Approximation

TL;DR

This paper applies the WKB approximation to analyze the energy spectrum of heavy mesons modeled as quark-antiquark pairs with the Cornell potential, providing an analytic approach to quarkonium energy levels.

Contribution

It introduces a Taylor series expansion technique around a specific point to simplify the potential, enabling an analytic WKB solution for heavy meson spectra.

Findings

Derived approximate energy levels for heavy mesons.

Validated the WKB method for quarkonium systems.

Provided insights into the quark confinement mechanism.

Abstract

In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and perform a Taylor series expansion around an appropriately chosen point $r_{0}$ to simplify the potential near the classical turning points. This expansion enables an analytic treatment of the Schr\"odinger equation within the leading-order WKB framework. The resulting quantization condition yields approximate energy levels that capture the essential dynamics of quarkonium systems and illustrate the utility of the WKB method in modeling hadronic bound states.