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

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 $0.036 {\rm GeV}^2 \le Q^2 \le 316 {\rm GeV}^2$.