Forward Elastic Scattering of Light on Light , γ + γ → γ + γ

The forward elastic scattering of light on light, i.e., the reaction γ + γ → γ + γ in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate ργγ , the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total γγ cross section data in the high energy region 5 GeV ≤ √ s ≤ 130 GeV, assuming a cross section that rises asymptotically as ln s. We then compare ργγ to ρnn, the ratio of the even portions of the pp and p̄p forward scattering amplitudes, as well as to ργp[1], the ρ value for Compton scattering. Within errors, we find that the three ρ-values in the c.m.s. energy region 5 GeV ≤ √ s ≤ 130 GeV are the same, as predicted by a factorization theorem of Block and Kadailov[2]. ∗Work partially supported by Department of Energy contract DA-AC02-76-Er02289 Task D. The purpose of this note is to analyze light on light elastic scattering at high energies, i.e., γ + γ → γ + γ, when the scattered γ is in the forward direction, in order to extract ργγ , the ratio of the real to the imaginary portion of the forward scattering amplitude, by using real analytic amplitudes. To the best of our knowledge, no one has either measured or calculated ργγ . Block and Kadailov[2] have shown that ρnn = ργp = ργγ if one uses eikonals for γγ, γp and the even portion of nucleon-nucleon scattering that have equal opacities, i.e., eikonals that have the same value at impact parameter b = 0 (for details of the assumptions made, see ref. [2]). This is the equivalent of the more physical statement that