Proton PDFs with non-linear corrections from gluon recombination

TL;DR

This paper investigates non-linear gluon recombination effects on proton PDFs, implementing corrections into the DGLAP equations, fitting to experimental data, and assessing their potential impact on future collider measurements.

Contribution

It introduces a numerical implementation of non-linear corrections to DGLAP evolution and constrains their strength using global deep inelastic scattering data.

Findings

No definitive evidence for non-linear effects in current data.

Recombination scale $Q_r$ is constrained to be less than approximately 2.5 GeV.

Future collider measurements could better constrain non-linear corrections.

Abstract

We present numerical studies of the leading non-linear 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 non-linear 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 non-linearities, 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 $Q_r \lesssim 2.5\,{\rm GeV}$. We also quantify the impact of the non-linear 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.