Orateur
Description
With the advent of the Electron-Ion Collider (EIC) and plans for the Large Hadron Electron Collider (LHeC), a clear understanding of the small-x regime of parton distribution functions (PDFs) is becoming increasingly important. In this kinematic region, the PDFs become very large and the linear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations are expected to become insufficient to describe the scale evolution of PDFs due to the rise of non-linear corrections proportional to $G^2/Q^2$.
We investigate the leading non-linear corrections to the DGLAP evolution equations resulting from gluon recombination, which reduce the pace of evolution at small momentum fractions $x$, while slightly increasing it at intermediate $x$. Implementing the momentum-conserving corrections derived by Zhu and Ruan in the xFitter framework allows us to carry out fits of proton PDFs using data on lepton-proton deep inelastic scattering from BCDMS, NMC and HERA. While the results show no indication of non-linearities, we are able to set limits on their strength in terms of the recombination scale $Q_r \lesssim 2.5$ GeV. While the non-linear corrections slow down the evolution, they do not improve the description of the longitudinal structure function $F_L(x,Q^2)$ data from HERA at small values of $Q^2$, which has have been difficult to reproduce with linear PDF fits.
Additionally, we show that planned measurements of $F_L(x,Q^2)$ at the EIC and the LHeC are expected to provide stronger constraints on the projected effects.
