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-$x$, $x\ensuremath{\le}0.01$, for all experimentally available values of ${Q}^{2}$, $0.045\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\le}{Q}^{2}\ensuremath{\le}800\text{ }\text{ }{\mathrm{GeV}}^{2}$. We show that the recent improvements resulting from the inclusion of running coupling corrections allow for a description of data in terms of 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 ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}.<1.1$. 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 $x={10}^{\ensuremath{-}12}$ is released as a computer code for public use.