An analysis of the Isgur-Wise Function and its derivatives within a Heavy-Light QCD Quark Model

TL;DR

This paper investigates the Isgur-Wise function within a heavy-light QCD quark model, addressing divergence issues in calculations by introducing cut-offs and analyzing the impact of polynomial approximations.

Contribution

It proposes a method to handle divergence in the Isgur-Wise function calculations by applying cut-offs and examines the effects of polynomial approximation on derivatives.

Findings

Introduction of cut-off values mitigates divergence issues.

Polynomial approximation order affects derivative calculations.

Results enhance understanding of heavy-light meson dynamics.

Abstract

In determining the mesonic wave function from QCD inspired potential model, if the linear confinement term is taken as parent (with columbic term as perturbation), Airy's function appears in the resultant wave function - which is an infinite series. In the study of Isgur-Wise function (IWF) and its derivatives with such a wave function, the infinite upper limit of integration gives rise to divergence. In this paper, we have proposed some reasonable cut-off values for the upper limit of such integrations and studied the subsequent effect on the results. We also study the sensitivity of the order of polynomial approximation of the infinite Airy series in calculating the derivatives of IWF.