A Higher Dimensional Potential Model Approach in the Study of Isgur-Wise Function for Heavy-Light Mesons

TL;DR

This paper develops a higher-dimensional potential model using string theory concepts to analyze the Isgur-Wise function for heavy-light mesons, incorporating the L"uscher term as a perturbation in the wave function calculation.

Contribution

It introduces a higher-dimensional potential approach with the L"uscher term as a perturbation to study meson wave functions and the Isgur-Wise function.

Findings

Derived meson wave functions in higher dimensions using Airy polynomial series.

Analyzed the impact of higher dimensions on the Isgur-Wise function and its derivatives.

Provided insights into the dimensional dependence of quark-antiquark potentials.

Abstract

Nambu-Goto action of 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 universal L\"{u}scher coefficient of the L\"uscher term $ \frac{\gamma}{r}$, which depends upon the space-time dimension `d'. We take linear term in potential as parent and L\"uscher term as perturbation for the generation of wave function for meson in d space-time dimension.The wave function comes out in terms of Airy's infinite polynomial series. With this wave function in higher dimension, we then study the Isgur-Wise function for heavy-light mesons and its derivatives.