Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction

TL;DR

The paper develops a QCD-inspired saturation framework for deep inelastic scattering at low $x$ and low to moderate $Q^2$ using a dipole picture, where the photon splits into a quark–antiquark pair that interacts with the proton via an $x$-dependent dipole cross section with a saturation radius $R_0(x)$. With only three parameters, the model reproduces DIS data for $x\le 0.01$ and extends plausibly into photoproduction, predicting an effective Pomeron intercept that evolves from soft to hard values and introducing a critical line $Q^2=1/R_0^2(x)$ marking saturation onset. Applying the framework to diffraction shows that the diffractive cross section shares the same leading small-$x$ behavior as the inclusive case for transverse photons, yielding a diffractive/inclusive cross-section ratio of a few percent that remains roughly constant with $x$ and $Q^2$. Charm is incorporated without introducing new parameters, shifting the saturation boundary to smaller scales and modestly increasing the low-$Q^2$ slope, while preserving overall agreement with a charm contribution to $F_2$.

Abstract

We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.

Figures (12)

• Figure 1: Diagrammatical representation of the basic process as discussed in the text.
• Figure 2: The profile of the dipole cross section for different $Q$. The small arrows below the figure show how the indicated parameters change when $Q$ decreases (for $W^2$ fixed).
• Figure 3: The $\gamma^* p$-cross section for various energies. The solid lines show the fit results with a light quark mass of 140MeV. The dotted lines show the cross section with the same parameters but with zero quark mass. The line across the curves indicates the position of the critical line.
• Figure 4: The logarithmic $Q^2$-slope of $F_2$ for fixed energies $W$, plotted as a function of $Q^2$ and $x$. The line across the curves shows the position of the critical line.
• Figure 5: The position of the critical line in the $(x,Q^2)$-plane. The narrow hatched area corresponds to the acceptance region of HERA. The wide hatched region indicates the range for a future $1~TeV$$ep$-collider. The boundaries are lines of constant $y$.