The mass of hadrons in the Regge trajectory scales as
$m=\sqrt{\frac{J}{\alpha}-\alpha_0}=\sqrt{\frac{n}{\alpha}-\alpha_0}\propto \sqrt{n}$,
where $J=n$ is the spin of the particle (in natural units, for zero angular momentum) and $\alpha$ is the inverse QCD string tension.
In the Kaluza Klein (KK) model, the mass scales as
$m=\frac{n}{R}\propto n$
where $R$ is the radius of the KK compactified dimension.
Can we obtain any relation between these two mass formulas, perhaps yielding a relation between the KK radius $R$ and the inverse string tension $\alpha$ in the Regge trajectory?
