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Using an eikonal analysis, we examine the validity of the factorizationtheorem for nucleon-nucleon, gamma p and gamma gamma collisions. As an example,using the additive quark model and meson vector dominance, we directly showthat for all energies and values of the eikonal, that the factorization theoremsigma_{nn}/sigma_{gamma p} = sigma_{gamma p}/sigma_{gamma gamma} holds. We canalso compute the survival probability of large rapidity gaps in high energypbar p and pp collisions. We show that the survival probabilities are identical(at the same energy) for gamma p and gamma gamma collisions, as well as fornucleon-nucleon collisions. We further show that neither the factorizationtheorem nor the reaction-independence of the survival probabilities depends onthe assumption of an additive quark model, but, more generally, depends on theopacity of the eikonal being independent of whether the reaction is n-n, gammap or gamma gamma.Comment: 8 pages, Revtex, no figures. Expanded discussion, minor correction

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Consequences of the factorization hypothesis in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo></mml:math><i>pp</i>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>p</mml:mi><mml:mo>,</mml:mo></mml:math>and γγ collisions

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