BFKL evolution and universal structure function at very small $x$

Abstract

The Balitskii-Fadin-Kuraev-Lipatov (BFKL) and the Gribov-Lipatov- Dokshitzer-Altarelli-Parisi (GLDAP) evolution equations for the diffractive deep inelastic scattering at ${1\over x} \gg 1$ are shown to have a common solution in the weak coupling limit: $F_{2}(x,Q^{2})\propto [\alpha_{S}(Q^{2})]^{-\gamma} \left({1\over x}\right)^{\Delta_{\Pom}}$. The exponent $\gamma$ and the pomeron intercept $\Delta_{\Pom}$ are related by $\gamma\Delta_{\Pom}={4\over 3}$ for the $N_{f}=3$ active flavors. The existence of this solution implies that there is no real clash between the BFKL and GLDAP descriptions at very small $x$. We present derivation of this solution in the framework of our generalized BFKL equation for the dipole cross section, discuss conditions for the onset of the universal scaling violations and analyse the pattern of transition from the conventional Double-Leading-Logarithm approximation for the GLDAP evolution to the BFKL evolution at large ${1\over x}$.