Consequences of the factorization hypothesis inp¯p,pp,γp,and γγ collisions

Using an eikonal analysis, we examine the validity of the factorization theorem for nucleon-nucleon, $\gamma p,$ 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 the factorization theorem ${\sigma }_{\mathrm{nn}}/{\sigma }_{\gamma p}={\sigma }_{\gamma p}/{\sigma }_{\gamma \gamma }$ holds. We can also compute the survival probability of large rapidity gaps in high energy $\overline{p}p$ and pp collisions. We show that the survival probabilities are identical (at the same energy) for $\gamma p$ 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, $\gamma p,$ or γγ.