The Color Dipole Picture of low-x DIS: Model-Independent and Model-Dependent Results

TL;DR

This paper analyzes the color-dipole picture of low-x deep inelastic scattering, distinguishing model-independent from model-dependent results, and shows consistency with experimental data across a wide range of Q^2 values.

Contribution

It provides a model-independent analysis of low-x DIS, deriving universal ratios and scaling behaviors, and extends the model-dependent approach to higher x values with experimental validation.

Findings

The ratio of longitudinal to transverse photoabsorption cross sections is approximately 0.27.

The total photoabsorption cross section exhibits specific scaling behaviors with the variable η.

The theoretical predictions align well with experimental data across a broad Q^2 range.

Abstract

We present a detailed examination of the color-dipole picture (CDP) of low-$x$ deep inelastic scattering. We discriminate model-independent results, not depending on a specific parameterization of the dipole cross section, from model-dependent ones. The model-independent results include the ratio of the longitudinal to the transverse photoabsorption cross section at large $Q^2$, or equivalently the ratio of the longitudinal to the unpolarized proton structure function, $F_L (x,Q^2)=0.27 F_2 (x, Q^2)$, as well as the low-$x$ scaling behavior of the total photoabsorption cross section $\sigma_{\gamma^*p} (W^2, Q^2)=\sigma_{\gamma^*p} (\eta (W^2, Q^2))$ as $\log (1 / \eta (W^2, Q^2))$ for $\eta (W^2, Q^2) <1$, and as $1/\eta (W^2, Q^2)$ for $\eta (W^2, Q^2) \gg 1$. Here, $\eta (W^2, Q^2)$ denotes the low-$x$ scaling variable, $\eta (W^2, Q^2)=(Q^2 + m^2_0) / \Lambda^2_{sat} (W^2)$ with $\Lambda^2_{sat} (W^2)$ being the saturation scale. The model-independent analysis also implies $\lim\limits_{W^2\rightarrow\infty, Q^2 {\rm fixed}} \sigma_{\gamma^*p} (W^2, Q^2) / \sigma_{\gamma p} (W^2) \rightarrow 1$ at any $Q^2$ for asymptotically large energy, $W$. Consistency with pQCD evolution determines the underlying gluon distribution and the numerical value of $C_2 = 0.29$ in the expression for the saturation scale, $\Lambda^2 (W^2) \sim (W^2)^{C_2}$. In the model-dependent analysis, by restricting the mass of the actively contributing $q \bar q$ fluctuations by an energy-dependent upper bound, we extend the validity of the color-dipole picture to $x \cong Q^2 / W^2 \le 0.1$. The theoretical results agree with the world data on DIS for $0.036 {\rm GeV}^2 \le Q^2 \le 316 {\rm GeV}^2$.