"Quark parton model, light-cone expansions and virtual γγ-scattering"

Abstract
Here a model like that of Landshoff and Polkinghorne is presented. Within it a method is formulated which allows one for producing an arbitrary number of currents to obtain an expansion when one of the distances is small. The model is applied to the study of the forward γγ-scattering in the region of deep virtuality of one of the photons : - q²₁ >> m²₀, q²₂ is arbitrary (q₁ and q₂ are photon momenta) (q₁ + q₂)² = s m₀ ~ 1 GeV. For the absorptive part of the amplitude the following results have been obtained : a) In the region m²₀ << s << p² q²/m²₀ the contribution of the box-diagram is dominant, and therefore amplitude is known. The eight independent invariant amplitudes of the process reduce to the two unknown functions in all the other cases. These last ones depend on two combinations of three independent variables s, q²₁ and q²₂ only. b) In the region s₀ ~ m²₀ these combinations are s/m²₀ and (q²₁ - q²₂)/(q²₁ + q²₂). c) In the region s > q²₁ q²₂/m²₀ these combinations are s/q²₁ and q²₂/m²₀. At q²₂/m²₀ >> 1 the dependence on only argument s m²₀/q²₁ q²₂ is left and at s m²₀/q²₁ q²₂ >> 1 the Regge behaviour takes place.