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, $F_L(x,Q^2)=0.27F_2(x,Q^2)$, as well as the low-$x$ scaling behavior of the total photoabsorption cross section ${\sigma }_{{\gamma }^{\ast }p}(W^2,Q^2)={\sigma }_{{\gamma }^{\ast }p}(\eta (W^2,Q^2))$ 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, $\eta (W^2,Q^2)=(Q^2+m_0^2)/{\Lambda }_{sat}^2(W^2)$ with ${\Lambda }_{sat}^2(W^2)$ being the saturation scale. The model-independent analysis also implies $\underset{W^2\to \infty ,Q^2\mathrm{fixed}}{\lim }{\sigma }_{{\gamma }^{\ast }p}(W^2,Q^2)/{\sigma }_{\gamma p}(W^2)\to 1$ 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 $0.036{\mathrm{GeV}}^2\le Q^2\le 316{\mathrm{GeV}}^2$.

77 pages, 30 figures

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