High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions
Adrian Dumitru🇺🇸 · Heikki Mäntysaari🇫🇮 · Risto Paatelainen🇫🇮
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 describing the scattering of a dipole with size off the target that is probed at momentum fraction . Rather than using ad hoc parameterizations tuned to high-energy data at , here we attempt to construct an initial scattering amplitude that is consistent with low-energy, large- properties of the proton. We start from a non-perturbative three quark light-cone model wave function from the literature. We add corrections due to the emission of a gluon, and 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 parameterizations of the resulting for . Solving the BK equation in the leading logarithmic (LL) approximation towards lower , we obtain a fair description of the charm cross section in deeply inelastic scattering measured at HERA by fitting one parameter, the coupling constant . However, without the option to tune the initial amplitude at , the fit of the high precision data results in at , providing clear statistical evidence for the need of systematic improvement e.g. of the photon wave function, evolution equation, and initial condition.