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

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 xx₀, 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 αₛ0.2. 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.