Isgur-Wise function in a QCD potential model with coulombic potential as perturbation

TL;DR

This paper models heavy-light mesons using a QCD-inspired potential, treating the linear confinement term as the main potential and the Coulombic part as a perturbation to compute the Isgur-Wise function and its properties.

Contribution

It introduces a perturbative approach with the linear potential as the main term and Coulombic part as perturbation to analyze the Isgur-Wise function in heavy-light mesons.

Findings

Calculated the slope and curvature of the Isgur-Wise function.

Used Airy functions as unperturbed wavefunctions.

Applied Dalgarno perturbation theory up to first order.

Abstract

We study heavy light mesons in a QCD inspired quark model with the Cornell potential$-\frac{4\alpha_{S}}{3r}+br+c$. Here we consider the linear term $br$ as the parent and $-\frac{4\alpha_{S}}{3r}+c$ i.e.the Coloumbic part as the perturbation.The linear parent leads to Airy function as the unperturbed wavefunction. We then use the Dalgarno method of perturbation theory to obtain the total wavefunction corrected upto first order with Coulombic peice as the perturbation.With these wavefunctions, we study the Isgur-Wise function and calculate its slope and curvature.