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

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.