Scaling and asymptotic behavior of the $\gamma^* p$ total cross section at low x

Abstract

The scaling in $\sigma_{\gamma^*p}$ cross sections (for $Q^2/W^2 << 1$) in terms of the scaling variable $\eta = (Q^2 + m^2_0)/\Lambda^2 (W^2)$ is interpreted in the generalized vector dominance/color-dipole picture (GVD/CDP). The quantity $\Lambda^2 (W^2)$ is identified as the average gluon transverse momentum absorbed by the $q \bar q$ state, $<\vec l^{~2}> = (1/6) \Lambda^2 (W^2)$. At any $Q^2$, for $W^2 \to \infty$, the cross sections for virtual and real photons become universal, $\sigma_{\gamma^*p}(W^2,Q^2)/\sigma_{\gamma p}(W^2) \to 1$. The gluon density corresponding to the color-dipole cross section in the appropriate limit is found to be consistent with the results from QCD fits.