Forward Elastic Scattering of Light on Light, \gamma+\gamma\to\gamma+\gamma

The forward elastic scattering of light on light, {\em i.e.,} the reaction $\gamma +\gamma \to \gamma +\gamma$ in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate ${\rho }_{\gamma \gamma }$, the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total $\gamma \gamma$ cross section data in the high energy region $5GeV\le \sqrt{s}\le 130$ GeV, assuming a cross section that rises asymptotically as ${\ln }^{2}s$. We then compare ${\rho }_{\gamma \gamma }$ to ${\rho }_{nn}$, the ratio of the even portions of the $pp$ and $\text{pbar}p$ forward scattering amplitudes, as well as to ${\rho }_{\gamma p}$, the $\rho$ value for Compton scattering. Within errors, we find that the three $\rho$-values in the c.m.s. energy region $5GeV\le \sqrt{s}\le 130$ GeV are the same, as predicted by a factorization theorem of Block and Kadailov.