Constrains on treating linear part as perturbation in a QCD Potential Model

TL;DR

This paper reviews perturbation approaches in QCD potential models, analyzing when the linear or Coulombic parts can be treated as perturbations, and finds optimal parameter ranges for each case.

Contribution

It provides a critical analysis of perturbation methods in QCD potential models, identifying parameter ranges where linear or Coulombic parts are better suited as perturbations.

Findings

Linear part can be treated as perturbation for higher s (0.37 to 0.75).

Better results with Coulombic perturbation for s .37.

Constant shift in potential improves model accuracy.

Abstract

We make a review of the different works of Quark Model which are based on Perturbation theory. We make a critical analysis of taking linear part of the Potential as perturbation with Coulombic part as parent and its reverse case. We find in the analysis that the linear part can be treated as perturbation for a set of larger values of $\alpha_{s}$ in the range $0.37 \leq \alpha_{s}\leq 0.75$ with a constant shift in the Cornell potential within range of $-0.4 GeV \leq c \leq -1 GeV$. Moreover with the same range of constant shift in the Potential, we expect better results with coulombic part as perturbation for $\alpha_{s}\leq 0.37$.