Forward elastic scattering of light on light, \gamma+\gamma->\gamma+\gamma

The forward elastic scattering of light on light, i.e., the reaction $\gamma+\gamma\rightarrow\gamma+\gamma$ 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 5 GeV $\le \sqrt s\le 130$ GeV, assuming a cross section that rises asymptotically as ln² s. We then compare $\rho_{\gamma \gamma} to \rho_{nn}$, the ratio of the even portions of the pp and $\bar pp$ forward scattering amplitudes, as well as to $\rho_{\gamma p}$ [1], the $\rho$ value for Compton scattering. Within errors, we find that the three $\rho$-values in the c.m.s. energy region 5 GeV$\le \sqrt s\le$ 130 GeV are the same, as predicted by a factorization theorem of Block and Kaidalov [2].