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

Abstract

The scaling in ${\sigma }_{{\gamma }^{\ast }p}$ cross sections (for $Q^2/W^2<<1$) in terms of the scaling variable $\eta =(Q^2+m_0^2)/{\Lambda }^2(W^2)$ 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, ${\sigma }_{{\gamma }^{\ast }p}(W^2,Q^2)/{\sigma }_{\gamma p}(W^2)\to 1$. 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.

Comments: 8 pages, Latex using psfig, 5 figures, documentclass elsart. Presented at IX Blois Workshop on Elastic and Diffractive Scattering, Pruhonice near Prague, Czech Republic, June 9-15, 2001