Masses of Heavy Flavour Mesons in a potential Model Approach with Wave Function containing Airy's Infinite Series

TL;DR

This paper calculates the masses of heavy-flavored mesons using a potential model with an Airy polynomial series wave function, introducing a cutoff to manage divergences, and achieves results close to experimental data.

Contribution

It presents a novel wave function approach involving Airy's infinite series for meson mass calculations within a potential model.

Findings

Ground state meson masses closely match PDG data.

Introduces a cutoff parameter to handle divergences in the wave function.

Demonstrates the effectiveness of Airy series in meson mass predictions.

Abstract

We report the masses of $B$ and $D$ sectors heavy-flavoured mesons obtained by using our recently developed meson wave function employing potential model approach with linear confinement term in potential as parent in the perturbation method. As the wave-function involves infinite Airy's polynomial series, in carrying out the mass calculation, to avoid divergences, we have introduced some cut-off parameter for inter-quark separation. Our results for ground state masses of heavy-flavoured $B$ and $D$ sector mesons are reasonably closer to the PDG masses.