An Analysis of the Isgur–wise Function and Its Derivatives Within a Heavy–light QCD Quark Model

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.

Isgur–Wise function and a new approach to potential model

“…It measures the overlap of the wave functions of the light degrees of freedom in the initial and final mesons moving with velocities v and v respectively. The calculation of Isgur-Wise function is non-perturbative in principle and is performed for different phenomenological wave functions for mesons [11,21]. This function depends upon the meson wave function and some kinematic factor, as given below :…”

“…We introduce u(r) = rR(r) and the dimensionless variable ρ(r) = (2µb) The unperturbed wave function [21] for ground state is 6) where N 0 is the normalization constant and The first order perturbed eigen function ψ (1) can be calculated using relation (A.6).…”

“…On the other hand in ref. [10,20,21], the Schrodinger equation is solved by considering the linear part to be dominant over the Coulombic part.…”

A Potential Model Approach in the Study of Static and Dynamic Properties of Heavy-Light Quark-Antiquark Systems

“…We have developed an approximate analytic ground state wave function of meson with Coulomb plus linear potential. In analogy to our previous works [15][16][17], here also we have studied the IWF of heavy-light mesons with this wave function. Regarding slope and curvature of IWF ( Table-1), we find that our results becomes better for heavier mesons.…”

“…In this paper, we propose a simpler form of analytic solution of Schrodinger equation with Cornell potential. Our earlier work with Cornell potential using perturbation technique [15][16][17]72,73], considering its linear confinement term as parent, we have found that Airy's infinite polynomial function appears in the solution for wave function. Based upon our past study, here we construct the analytic form of the meson wave function for linear plus Coulombic potential in terms of Airy's function.…”