Improved wave function for heavy-light mesons in QCD potential model approach and parameterization of the Cornell potential

TL;DR

This paper develops an improved wave function for heavy-light mesons within the QCD potential model, refining the Cornell potential parameters and analyzing inter-quark separations to enhance understanding of meson properties.

Contribution

It introduces a multiplicative method for solving the Schrödinger equation, providing a more accurate wave function and parameterization of the Cornell potential for heavy-flavored mesons.

Findings

Refined range of the scale factor c for the Cornell potential.

Identification of critical inter-quark separation influencing perturbation terms.

Enhanced understanding of meson wave functions in QCD models.

Abstract

We report improved wave function for mesons in QCD potential model approach using multiplicative method for solution of Schr\"{o}dinger equation for the extreme cases of inter-quark separations ($r\rightarrow0$ and $r\rightarrow\infty$). Using the wave function we find the range of the scale factor c of the Cornell potential with reference to the mass scale of B and D sectors heavy-flavoured mesons. With our computed range of c, we also explore the critical inter-quark separation which should govern the choice of parent-child terms in perturbation method out of the linear and Coulombic terms of the Cornell potential.