Structure function of the nucleus in the perturbative QCD with $N_c\rightarrow\infty$ (BFKL pomeron fan diagrams)

Abstract.

The equation for the sum of BFKL pomeron fan diagrams is rederived by a direct summation and solved numerically for rapidities $y\leq 50$. At high rapidities, $y>20$, the resulting cross-sections for the scattering of a longitudinally polarized $q\bar q$ pair on the nucleus cease to depend on its transverse dimension and tend to a constant limit of $0.1768 R_A^2$, which corresponds to scattering of a color dipole on a black disk. Thus the unitarity is restored and the singularity in the j plane is reduced to a simple pole at $j=1$. The nuclear structure function at small x behaves as $Q^2\ln(1/x)$. The gluon density found has a soliton-like form in the log k space: its form is close to Gaussian, independent of rapidity, the center moving towards higher log k with a nearly constant velocity as the rapidity increases.