Modified Coulomb potential and the S-state wavefunction of heavy quarkonia

TL;DR

This paper addresses the singularity issue in S-wave wavefunctions of heavy quarkonia caused by relativistic kinematics combined with Coulomb potentials, proposing a method to resolve it while maintaining phenomenological accuracy.

Contribution

The authors introduce a novel approach to eliminate wavefunction singularities at the origin in relativistic Coulomb problems for heavy quarkonia.

Findings

Successfully removes wavefunction singularity at the origin.

Maintains the phenomenological success of relativistic models.

Applicable to atomic, nuclear, and particle physics problems.

Abstract

The combination of relativistic kinematics together with Coulomb or Yukawa potentials is a common place in atomic, nuclear and meson mass phenomenology. In meson spectroscopy, linear and Coulomb-like potentials are the most commonly used potentials and decays rates are also calculated using the value of the wavefunction at the origin. But, it has been known for sometime that the use of relativistic kinematics together with Coulomb or Coulomb-like potentials produces wavefunction singularity at the origin for S-wave \cite{DuranFriarPolyzou}. Therefore, there is a need to address this problem somehow. In this letter, we show how to overcome this problem without destroying the phenomenological success of the use of relativistic kinematics in meson mass spectroscopy. Our method can be easily implemented for similar problems in atomic, nuclear and particle phenomenology.