Isgur-Wise function within a QCD quark model with Airy's function as the wave function of heavy-light mesons

TL;DR

This paper develops an improved wave function for heavy-light mesons using a QCD potential with linear confinement and Coulombic perturbation, deriving the Isgur-Wise function and its derivatives with Airy's function appearing in the wave function.

Contribution

It introduces a novel wave function incorporating Airy's series in a QCD potential model to compute the Isgur-Wise function for heavy-light mesons.

Findings

Derived the Isgur-Wise function within the new wave function framework.

Calculated derivatives of the Isgur-Wise function for heavy-light mesons.

Demonstrated the appearance of Airy's function in meson wave functions.

Abstract

We report some improved wave function for mesons taking linear confinement term in standard QCD potential as parent and Coulombic term as perturbation while applying quantum mechanical perturbation technique in solving Schrodinger equation with such a potential. We find that Airy's infinite series appears in the wave-function of the mesons. We report our calculations on the Isgur-Wise function and its derivatives for heavy-light mesons, within this framework.