S-matrix unitarity, impact parameter profiles, gluon saturation and high-energy scattering

Abstract

A model combining perturbative and non-perturbative QCD is developed to compute high-energy reactions of hadrons and photons and to investigate saturation effects that manifest the S-matrix unitarity. Following a functional integral approach, the S-matrix factorizes into light-cone wave functions and the universal amplitude for the scattering of two color-dipoles which are represented by Wegner–Wilson loops. In the framework of the non-perturbative stochastic vacuum model of QCD supplemented by perturbative gluon exchange, the loop–loop correlation is calculated and related to lattice QCD investigations. With a universal energy dependence motivated by the two-pomeron (soft + hard) picture that respects the unitarity condition in impact parameter space, a unified description of pp, πp, Kp, γ∗p, and γγ reactions is achieved in good agreement with experimental data for cross sections, slope parameters, and structure functions. Impact parameter profiles for pp and γ∗Lp reactions and the gluon distribution of the proton xG(x,Q2,|b→⊥|) are calculated and found to saturate in accordance with S-matrix unitarity. The c.m. energies and Bjorken x at which saturation sets in are determined.