# A model of mesons in finite extra-dimension

## TL;DR

This paper explores the stability of heavy flavoured mesons in finite extra dimensions, deriving a QCD Bohr radius and analyzing mass implications, suggesting extra dimensions are constrained within current experimental limits.

## Contribution

It introduces a model linking meson stability to extra-dimensional size and calculates the allowed range of extra dimensions based on meson mass data.

## Key findings

- Meson stability in extra dimensions is achieved for size $R \,\leq\, a_0/4$.
- The QCD Bohr radius in extra dimensions is within current experimental limits.
- Allowed extra dimension size is $L \leq 10^{-16}$ m, below current limits.

## Abstract

Recently,problem of stability of H-atom has been reported in extra-finite dimension,and found out that it is stable in extra-finite dimension of size,$R\leq\frac{a_0}{4}$,where,$a_0$ is the Bohr radius.Assuming that,the heavy flavoured mesons have also such stability controlled by the scale of coupling constant,we obtain corresponding QCD Bohr radius and it is found to be well within the present theoretical and experimental limit of higher dimension.We then study its consequences in their masses using effective string inspired potential model in higher dimension pursued by us.Within the uncertainty of masses of known Heavy Flavoured mesons the allowed range of extra dimension is $L\leq10^{-16}m$,which is well below the present theoretical and experimental limit,and far above the Planck length $\simeq1.5\times10^{-35}$ m.