### BOUNDS ON FINITE EXTRA-DIMENSION FROM THE MASSES OF LIGHT-HEAVY MESONS IN A QCD POTENTIAL MODEL

#### Abstract

Recently, the problem of stability of the 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. Motivated by this, we assume that the light-heavy mesons also have such stability controlled by the scale of coupling constant, and we obtain corresponding QCD Bohr radius, $R_{QCD}\leq\frac{a_0\mid_{QCD}}{4}$, where $a_0=\frac{4\alpha_s}{3}$, and $\alpha_s$ is the strong coupling constant and $\mu$ is the reduced mass of mesons, and it is found to be well within the present theoretical and experimental limit of higher dimension. We then, obtain the wave function of light-heavy mesons considering the well known linear plus coulomb, Cornell potential in a space with one finite extra-dimension. Specifically, we consider one finite extra dimension and calculate the masses of few light-heavy mesons. Comparing our results with the well-known experimental data,we obtain the bound on the size of extra-dimension, which is well within the present theoretical and experimental bound.

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