Perturbative saturation and the soft Pomeron

Abstract

We show that perturbation theory provides two distinct mechanisms for the power like growth of hadronic cross sections at high energy. One, the leading BFKL effect is due to the growth of the parton density, and is characterized by the leading BFKL exponent. The other mechanism is due to the infrared diffusion, or the long range nature of the Coulomb field of perturbatively massless gluons. When perturbative saturation effects are taken into account, the first mechanism is rendered ineffective but the second one persists. We suggest that these two distinct mechanisms are responsible for the appearance of two pomerons. The density growth effects are responsible for the hard pomeron and manifest themselves in small systems (e.g. gamma^* or small size fluctuations in the proton wave function) where saturation effects are not important. The soft pomeron is the manifestation of the exponential growth of the black saturated regions which appear in typical hadronic systems. We point out that the nonlinear generalization of the BFKL equation which takes into account wave function saturation effects ("pomeron loops") provides a well defined perturbative framework for the calculation of the soft pomeron intercept. The conjecture of a perturbative soft pomeron is consistent with picturing the proton as a loosely bound system of several small black regions corresponding e.g. to constituent quarks of size about 0.3 fm. Phenomenological implications of this picture are compatible with the main qualitative features of data on p-p scattering.