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

Abstract

Equation for the sum of BFKL pomeron fan diagrams is rederived by direct summation and solved numerically for rapidities y ≤ 50. At high rapidities y > 20 the resulting crosssections for the scattering of a longitudinally polarized qq pair on the nucleus cease to depend on its transverse dimension and tend to a constant limit 0.1768 R 2 A , 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 Q 2 ln(1/x). The found gluon density 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 rapidity increases.

Running coupling and power corrections in non-linear evolution at the high-energy limit

“…Such prescriptions have been assumed in all numerical simulation of the BK equation [33,45,[72][73][74][75][76][77]. Similar assumptions were used in the analytical estimates of Ref.…”

Pomeron interaction in the perturbative QCD

“…For fan diagrams Fig. 2, left, there exists an alternative derivation in the dipole picture, which, translated into the BFKL language, indicated that indeed in consecutive splittings exactly vertices Γ appear [13,14]. However in view of the rather indirect correspondence between the dipole and BFKL approaches it would be desirable to derive this result within the latter approach.…”

Pomeron fan diagrams in perturbative QCD

“…the scattering of a projectile on three color singlet targets. In earlier demonstrations [14] it was tacitly assumed that in consecutive splittings exactly the same vertices Γ appear. An explicit derivation, however, is still missing.…”