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

M. A. Braun

Paper

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

Abstract

Equation for the sum of BFKL pomeron fan diagrams is rederived by direct summation and solved numerically for rapidities

. At high rapidities y>20 the resulting cross-sections for the scattering of a longitudinally polarized

pair on the nucleus cease to depend on its transverse dimension and tend to a constant limit 0.1768

, which corresponds to scattering of a colour 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

. The found gluon density has a soliton-like form in the

space: its form is close to Gaussian, independent of rapidity, the centermoving towards higher

with a nearly constant velocity as rapidity increases.