High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions

Abstract

The forward scattering amplitude of a small dipole at high energies is given in the mean field approximation by the Balitsky-Kovchegov (BK) evolution equation. It requires an initial condition N(r;x0) describing the scattering of a dipole with size r off the target that is probed at momentum fraction x0. Rather than using ad hoc parametrizations tuned to high-energy data at x≪x0, here we attempt to construct an initial scattering amplitude that is consistent with low-energy, large-x properties of the proton. We start from a nonperturbative three quark light-cone model wave function from the literature. We add O(g) corrections due to the emission of a gluon, and O(g2) virtual corrections due to the exchange of a gluon, computed in light-cone perturbation theory with exact kinematics. We provide numerical data as well as analytic parametrizations of the resulting N(r;x0) for x0=0.01–0.05. Solving the BK equation in the leading logarithmic approximation towards lower x, we obtain a fair description of the charm cross section in deeply inelastic scattering measured at HERA by fitting one parameter, the coupling constant αs≃0.2. However, without the option to tune the initial amplitude at x0, the fit of the high precision data results in χ2/Ndof=2.3 at Ndof=38, providing clear statistical evidence for the need of systematic improvement, e.g., of the photon wave function, evolution equation, and initial condition.