RMS and charge radii in a potential model

TL;DR

This paper employs Dalgarno's perturbation method to solve the Schrödinger equation with the Cornell potential, deriving bounds on meson radii and exploring their relation to charge radii.

Contribution

It introduces a novel approach to incorporate short and long-range effects in meson wave functions using dual scales within a potential model.

Findings

Bounds on r.m.s. radii for heavy mesons are reported.

The relation between r.m.s. and charge radii of mesons is established.

Method effectively accounts for potential's range effects.

Abstract

The Dalgarno's method of perturbation is used to solve the Schrodinger's equation with the Cornell potential $V(r)=-\frac{4\alpha_s}{3r}+br+c$. The short range and long range effect of the potential is incorporated in the same wave function by using two scales $r^S$ and $r^L$ as an integration limit. The results for bounds on r.m.s. radii of various heavy flavored mesons are reported. We have also showed the relation between r.m.s. and charge radius of mesons.