Non-linear BFKL dynamics: Color screening vs. gluon fusion

Abstract

A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken x is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is R c ≃ 0.2 − 0.3 fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter ∼ R 2 c /8B, with the diffraction cone slope B standing for the characteristic size of the interaction region. It should slowly ∝ 1/ ln Q 2 decrease at large Q 2 . Smallness of the ratio R 2 c /8B makes the non-linear effects rather weak even at lowest Bjorken x available at HERA. We report the results of our studies of the non-linear BFKL equation which has been generalized to incorporate the running coupling and the screening radius R c as the infrared regulator.

Color screening, absorption, and σ tot pp at LHC

“…In [9] we found that the choice R c = 0.26 fm leads to a very good description of the DIS data on the proton structure function F 2 (x, Q 2 ) at small x. Applying the color dipole factorization to σ pp tot we observe (see Fig.…”

“…At superhigh energies, E Lab > 10 4 − 10 5 GeV, the perturbative component starts taking over and its unitarization becomes a central issue. In [8,9,10] it was demonstrated that the non-linear, i.e., unitarity effects are very sensitive to the IR regularization which defines a transition between the nonperturbative and perturbative domains. Empirically, the bulk of the total cross section at E Lab ∼ 10 4 −10 5 GeV comes from the nonperturbative domain and our analysis suggests rather small, infrared cutoff for the perturbative contribution, R c = 0.26 fm.…”

“…The simplest way to take them into account was suggested first in [6,7]. In [9] the BK equation was rederived in terms of the qq-nucleon partial-wave amplitudes (profile functions) and for the predominantly imaginary elastic dipole-nucleon amplitude f (ξ, r, k) = iσ(ξ, r) exp(−Bk 2 /2) upon integrating over the impact parameters it was reduced to the following form [9] …”

“…absorption corrections to the BFKL evolution are described by the non-linear BK equation [6,7]. The strength of non-linear effects depends crucially on the IR cutoff R c [8,9,10]. Hence, one more issue we address in this communication is the role of the absorption corrections to σ pp tot and the non-linear dynamics of the perturbative component of pp-interactions at the LHC energies.…”

BFKL, BK and the infrared

“…The perturbative gluons with short propagation length do not walk to large distances, where they supposedly fuse together [6]. The fusion probability appears to be controlled by the dimensionless parameter R 2 c /8B, where B stands for the diffraction cone slope [7,8]. In this communication we discuss the BFKL [2], BK [6] phenomenology of DIS in presence of finite correlation length R c with particular emphasis on a sharpened sensitivity of the non-linear effects to the infrared.…”