An Analysis of Isgur-Wise Function of Heavy-Light Mesons within a Higher Dimensional Potential Model Approach

TL;DR

This paper investigates the Isgur-Wise function for heavy-light mesons using higher-dimensional wave functions derived from a potential inspired by string theory, comparing perturbation methods with different parent potentials.

Contribution

It introduces a higher-dimensional approach to compute meson wave functions and analyzes the Isgur-Wise function, comparing perturbation techniques with different parent potentials.

Findings

Higher-dimensional wave functions are successfully used to analyze the Isgur-Wise function.

The study compares the effectiveness of perturbation methods with different parent potentials.

Results highlight the impact of dimensionality and perturbation choice on meson property calculations.

Abstract

Nambu-Goto action for bosonic string predicts the quark-antiquark potential to be $V(r) = -\frac{\gamma}{r}+ \sigma r + \mu_0$. The coefficient $\gamma=\frac{\pi(d-2)}{24}$ is the L\"{u}scher coefficient of the L\"{u}scher term $\frac{\gamma}{r}$, which depends upon the space-time dimension `d'. Very recently, we have developed meson wave functions in higher dimension with this potential from higher dimensional Schrodinger equation by applying quantum mechanical perturbation technique with both $L\ddot{u}scher$ term as parent and as perturbation. In this letter, we analyze Isgur-Wise function for heavy-light mesons using these wave functions in higher dimension and make a comparative study on the status of the perturbation technique in both the cases.