Geometric scaling for the total gamma^* p cross section in the low x region

TL;DR

It is shown that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2), and it is suggested that the geometric scaling is more general than the saturation model.

Abstract

We observe that the saturation model of deep inelastic scattering, which successfully describes inclusive and diffractive data at small x, predicts a geometric scaling of the total gamma^* p cross section in the region of small Bjorken variable x. The geometric scaling in this case means that the cross section is a function of only one dimensionless variable tau = Q^2 R_0^2(x), where the function R_0(x) (called saturation radius) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q^2. We suggest that the geometric scaling is more general than the saturation model.

Figures (4)

• Figure 1: Experimental data on $\sigma_{\gamma^* p }$ from the region $x<0.01$ plotted versus the scaling variable $\tau=Q^2 R_0^2(x)$.
• Figure 2: $\sqrt{\tau} \sigma_{\gamma^* p}$ plotted versus the scaling variable $\tau$
• Figure 3: The lines corresponding to different values of scaling variable $\tau$ (continues curves) in the $(x,Q^2)$-plane. The points correspond to available experimental data located within the bins $\ln(\tau) \pm \delta$ ($\delta=0.1$) for each value of $\tau$. The numbers correspond to the value of $\tau$ for each curve.
• Figure 4: Experimental data on $\sigma_{\gamma^* p}$ from the region $x>0.01$ plotted versus the scaling variable $\tau=Q^2 R_0^2(x)$.