Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution

We perform a global fit to the structure function F_2 measured in lepton-proton experiments at small values of Bjorken-x, x\le 0.01, for all experimentally available values of Q^2, 0.045 GeV^2\le Q^2 \le 800 GeV^2. We show that the recent improvements resulting from the inclusion of running coupling corrections allow for a description of data in terms of non-linear 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 excellent fits to data with \chi^2/d.o.f.<1.1. Data for the proton longitudinal structure function F_L, not included in the fits, are also well described. We provide predictions for F_2 and F_L in the kinematical regions of interest for future colliders and ultra-high energy cosmic rays. Our analysis allows to perform a first principle extrapolation of the proton-dipole scattering amplitude. A numerical implementation of our results down to x=10^{-12} is released as a computer code for public use.