Proton PDFs with nonlinear corrections from gluon recombination

We present numerical studies of the leading nonlinear corrections to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations of parton distribution functions (PDFs) resulting from gluon recombination. The effect of these corrections is to reduce the pace of evolution at small momentum fractions $x$ while slightly increasing it at intermediate $x$. By implementing the nonlinear evolution in the xfitter framework, we have carried out fits of proton PDFs using data on lepton-proton deep inelastic scattering from HERA, BCDMS, and NMC. While we find no evidence for the presence of nonlinearities, they cannot be entirely excluded either, and we are able to set limits for their strength. In terms of the recombination scale $Q_r$, which plays a similar role as the saturation scale in the dipole picture of the proton, we find that $Q_r\lesssim 2.5\mathrm{GeV}$. We also quantify the impact of the nonlinear terms for the longitudinal structure function at the Electron-Ion Collider and the Large Hadron Electron Collider and find that these measurements could provide stronger constraints on the projected effects.