A Modification of the Saturation Model: DGLAP evolution

TL;DR

The paper addresses the mismatch between the original GBW saturation model and QCD scaling violations at high Q^2 by embedding DGLAP evolution of the gluon density into the small-r part of the dipole cross section. The authors derive a modified cross section with μ^2 = C/r^2 + μ0^2 and LO DGLAP-evolved xg(x, μ^2), preserving large-r saturation and the successful description of DIS diffraction. Global fits to HERA DIS data show improved agreement at large Q^2, with two viable parameterizations: one featuring a rising gluon density at small x and another with a valence-like initial gluon density, each yielding competitive χ^2 values. The work demonstrates a feasible route to merge saturation ideas with DGLAP evolution and preserves the predictive power for diffractive processes, suggesting further exploration of exclusive final states and a deeper QCD grounding.

Abstract

We propose to modify the saturation model of Golec-Biernat and Wusthoff by including DGLAP evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q^2 region. The successful description of DIS diffraction is preserved.

Figures (9)

• Figure 1: $F_2$ as a function of $x$ for fixed low $Q^2$ values. The comparison with the low $Q^2$ data from ZEUS. The solid lines: the model with the DGLAP evolution (\ref{['eq:sighatnew']}) (FIT 1) and the dotted lines: the saturation model (\ref{['eq:sighat']}).
• Figure 2: H1 and ZEUS data on $F_2$ as a function of $x$ for fixed values of $Q^2>1~\hbox{\rm GeV}^2$ and the saturatiom model curves. The solid lines: the model with the DGLAP evolution (\ref{['eq:sighatnew']}) (FIT 1) and the dotted lines: the saturation model (\ref{['eq:sighat']}).
• Figure 3: The effective slope $\lambda(Q^2)$ from the parameterization $F_2\sim x^{-\lambda(Q^2)}$ as a function of $Q^2$. The model with the DGLAP evolution (\ref{['eq:sighatnew']}): the solid line (FIT 1) and the dotted line (FIT 2). The saturation model (\ref{['eq:sighat']}): the dashed line. The open circles: ZEUS analysis and the full circles: H1 data H1SLOPES.
• Figure 4: The $\gamma^* p$ cross section as a function of energy $W^2$ at various $Q^2$. The solid lines: the model with the DGLAP evolution (\ref{['eq:sighatnew']}) (FIT 1) and the dotted line: the saturation model (\ref{['eq:sighat']}), shown for $x<0.01$.
• Figure 5: $F_2(x,Q^2)$ as a function of $Q^2$ for fixed $y=Q^2/(s x)$. The solid lines: the model with DGLAP evolution (\ref{['eq:sighatnew']}) (FIT 1) and the dashed lines: the saturation model (\ref{['eq:sighat']}). The curves are plotted for $x<0.01$. Full circles: ZEUS data and open circles: H1 data.