Nonlinear QCD meets data: A global analysis of lepton-proton scattering with running coupling Balitsky-Kovchegov evolution

We perform a global fit to the structure function F-2 measured in lepton-proton experiments at small values of Bjorken-x, x <= 0.01, for all experimentally available values of Q(2), 0.045 GeV2 <= Q(2) <= 800 GeV2. We show that the recent improvements resulting from the inclusion of running coupling corrections allow for a description of data in terms of nonlinear QCD evolution equations. In this approach F-2 is calculated within the dipole model with all Bjorken-x dependence described by the running coupling Balitsky-Kovchegov equation. Two different initial conditions for the evolution are used, both yielding good fits to data with chi(2)/d.o.f. <1.1. The proton longitudinal structure function F-L, not included in the fits, is also well described. Our analysis allows to perform a first principle extrapolation of the proton-dipole scattering amplitude once the initial condition has been fitted to presently available data. We provide predictions for F-2 and F-L in the kinematical regions of interest for future colliders and ultra-high energy cosmic rays. A numerical implementation of our results down to x = 10(-12) is released as a computer code for public use.