Perturbative QCD Evolution and Color Dipole Picture

Abstract

The proton structure function in the diffraction region of small Bjorken-$x$ and $10 {\rm GeV}^2 \le Q^2 \le 100 {\rm GeV}^2$ behaves as $F_2 (x, Q^2) = F_2 (W^2) = f_0 \cdot (W^2)^{C_2}$, where $x = Q^2 / W^2$. The exponent $C_2$ of the $\gamma^* p$ center-of-mass energy squared, $W^2$, is predicted from evolution of the flavor-singlet quark distribution, $C_2 = 0.29$, and the only free parameter, the normalization $f_0 = 0.063$, is fitted. The evolution of the gluon density multiplied by $\alpha_s (Q^2)$ is dentical to the evolution of the flavor-singlet quark density. This simple picture is at variance with the standard approach to evolution based on the coupled equations of flavor-singlet and gluon density.