ar X iv : h ep - p h / 03 01 08 4 v 1 1 3 Ja n 20 03 From Static Potentials to High - Energy Scattering

γ * L p Reaktionen und die stossparameterabhängige Gluonverteilung des Protons xG(x, Q 2 , | b ⊥ |) zeigen Sättigung bei extrem hohen Energien in¨Ubereinstimmung mit Unitaritätsgrenzen. Abstract We develop a loop-loop correlation model for a unified description of static color dipole potentials , confining QCD strings, and hadronic high-energy reactions with special emphasis on saturation effects manifesting S-matrix unitarity at ultra-high energies. The model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which describes color confinement via flux-tube formation of color fields. We compute the chromo-field distributions of static color dipoles in various SU (N c) representations and find Casimir scaling in agreement with recent lattice QCD results. We investigate the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements in lattice QCD. In this approach we compute high-energy dipole-dipole scattering with the Euclidean loop-loop correlation model. Together with a universal energy dependence and reaction-specific wave functions, the result forms the basis for a unified description of pp, πp, Kp, γ * p, and γγ reactions in good agreement with experimental data for cross sections, slope parameters, and structure functions. The obtained impact parameter profiles for pp and γ * L p reactions and the impact parameter dependent gluon distribution of the proton xG(x, Q 2 , | b ⊥ |) show saturation at ultra-high energies in accordance with unitarity constraints.