Linear vs non-linear QCD evolution: from HERA data to LHC phenomenology

TL;DR

The paper tests whether linear DGLAP or non-linear rcBK evolution better describes small-x DIS data from HERA, and assesses the impact on LHC predictions. It systematically compares the two formalisms by applying kinematic cuts that bias each approach and by examining extrapolations to unfitted regions. rcBK fits show stability under cuts and smaller deviations in small-x predictions, while DGLAP exhibits greater sensitivity and larger uncertainties when small-x data are removed. The results argue for a combined framework that accounts for both Q^2 evolution and small-x non-linear dynamics, with implications for precision collider phenomenology and future facilities like the LHeC or EIC.

Abstract

The very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascertained. We present a study of the dependence of the AAMQS fits, based on the running coupling BK non-linear evolution equations (rcBK), on the fitted dataset. This allows for the identification of the kinematical region where rcBK accurately describes the data, and thus for the determination of its applicability boundary. We compare the rcBK results with NNLO DGLAP fits, obtained with the NNPDF methodology with analogous kinematical cuts. Further, we explore the impact on LHC phenomenology of applying stringent kinematical cuts to the low-x HERA data in a DGLAP fit.

Figures (10)

• Figure 1: Sketch of the kinematic plane with cuts for DGLAP and rcBK fits. The arrows indicate backwards evolution in either formalism to the unfitted test region.
• Figure 2: Comparison between the NNPDF2.1 NNLO PDFs with $A_{\rm cut}=1.5$ and $A_{\rm cut}=0$ for the gluon (left plots) and the quark singlet (right plots). We perform the comparison of the absolute PDFs at the initial scale $Q^2_0=2$ GeV$^2$ in the upper plots, and we compare the ratio with respect the reference set at a typical LHC scale $Q^2=10^4$ GeV$^2$ in the lower plots.
• Figure 3: Distances between PDF central values as a function of the scale $Q^2$ of the PDFs. We show the results for the quark singlet PDF (left plot) and for the gluon PDF (right plot).
• Figure 4: Comparison of the result for reduced cross section obtained with rcBK fits with different cuts: $x_{\rm cut}=10^{-2},\, 3\cdot 10^{-3},\,10^{-3},\, 3\cdot10^{-4}$ and $10^{-4}$ and HERA data for four different bins in $Q^{2}=2.7,\,8.5,\,15$ and 35 GeV$^{2}$.
• Figure 5: Reduced cross section obtained with the rcBK cut fit with $x_{\rm cut}=10^{-4}$ and the DGLAP fit with $A_{\rm cut}=1.5$, compared to the experimental HERA-I data. The comparison is shown in four different bins in $Q^{2}=3.5,\,8.5,\,12$ and 18 GeV$^{2}$. In the DGLAP case the band corresponds to the PDF uncertainties.