Parameterisation space for Cornell potential in a QCD potential model

TL;DR

This paper analyzes the free parameters of the Cornell potential in QCD models, providing a parameter space for the strong coupling constant and constant shift to treat the confining part as a perturbation in heavy-light mesons.

Contribution

It offers a detailed parameterization space for the Cornell potential parameters, enabling better treatment of the confining part as a perturbation in meson models.

Findings

Wide range of alpha_s values (0.20 to 0.64) suitable for perturbation treatment.

Constant shift c ranges from -1.2 to -0.66 for the models.

Parameter space aids in consistent modeling of heavy-light mesons.

Abstract

We make a critical analysis on the free parameters of the Cornell potential $-4\alpha_{s}/3r+br+c$ and provide a parameterisation space for the strong coupling constant $\alpha_{s}$ and the constant shift $c$ for choosing linear part as perturbation in the potential model. In the analysis of heavy-light mesons $(D,D_{s},B,B_{s}~ \text{and} ~B_{c})$, we have found a wide range of values for the coupling constant i.e $0.20 \leq \alpha_{s}\leq 0.64$ with $-1.2 \leq c \leq -0.66$ which can be used to treat the confining part as perturbation.