Abstract
In this paper we developed approach based on the BFKL evolution in $\ln\Lb Q^2\Rb$. We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good $\chi^2/d.o.f. \approx 1.3$. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at $Q^2 = 0.25\,GeV^2$; (ii) the scattering amplitude at $Q^2 = 0.25\,GeV^2$ cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions.
Highlights
BFKL equation with running αS as the evolution equation2.1 The equation The NLO BFKL equation can be written in the form (see [9, 10, 21, 22])
With N (r, b : Y ) being the imaginary part of the scattering amplitude of the dipole with size x
We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good χ2/d.o.f. ≈ 1.3
Summary
2.1 The equation The NLO BFKL equation can be written in the form (see [9, 10, 21, 22]). One can see that in eq (2.1) we do not use the triumvirate structure [24,25,26,27] of the LO BFKL for running αS which looks as follows:. The advantage of this expression that it preserves the bootstrap equations for the reggeized gluon that has been proven in the NLO BFKL approach [23]. Since the main goal of this paper to clarify some rather qualitative features of the BFKL dynamics with running QCD coupling we feel it is reasonable to use the LO contribution to the simple equation (see eq (2.1)) following the example of refs. With αS (k⊥) and KLO are given by eq (2.3) and eq (2.4), respectively
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