Consequences of the Factorization Hypothesis in p̄p , pp , γp and γγ Collisions

Using an eikonal analysis, we examine the validity of the factorization theorem for nucleon-nucleon, γp and γγ collisions. As an example, using the additive quark model and meson vector dominance, we directly show that for all energies and values of the eikonal, that the factorization theorem σnn/σγp = σγp/σγγ holds. We can also compute the survival probability of large rapidity gaps in high energy p̄p and pp collisions. We show that the survival probabilities are identical (at the same energy) for γp and γγ collisions, as well as for nucleon-nucleon collisions. We further show that neither the factorization theorem nor the reaction-independence of the survival probabilities depends on the assumption of an additive quark model, but, more generally, depends on the opacity of the eikonal being independent of whether the reaction is n-n, γp or γγ. In this note, we will use an eikonal model to make calculations of cross sections and survival probabilities of rapidity gaps in nucleon-nucleon, γp and γγ collisions. In an eikonal model [1], we define our (complex) eikonal χ(b, s) so that a(b, s), the (complex) scattering amplitude in impact parameter space b, is given by a(b, s) = i 2 (