Unitarization of the BFKL Pomeron on a Nucleus

TL;DR

This paper shows that summing all fan diagrams in the Mueller dipole framework yields a nonlinear evolution equation that unitarizes the BFKL Pomeron on a nucleus. A perturbative series in the single-pomeron contribution converges outside the saturation region, while inside saturation the forward amplitude saturates to a constant, leading to F_2 growing only as $F_2 \propto \, \ln s$. The diffractive structure function F_2^D is likewise resummed and exhibits a black-disk limit where $F_2 = 2F_2^D$. The results provide a coherent picture of small-x dynamics, saturation, and diffraction in high-energy DIS on nuclei, with implications for gluon distributions and potential extensions to NLO running coupling corrections.

Abstract

We analyze the evolution equation describing all multiple hard pomeron exchanges in a hadronic or nuclear structure functions that was proposed earlier. We construct a perturbation series providing us with an exact solution to the equation outside of the saturation region. The series demonstrates how at moderately high energies the corrections to the single BFKL pomeron exchange contribution which are due to the multiple pomeron exchanges start unitarizing total deep inelastic scattering cross section. We show that as energy increases the scattering cross section of the quark-antiquark pair of a fixed transverse separation on a hadron or nucleus given by the solution of our equation inside of the saturation region unitarizes and becomes independent of energy. The corresponding F_2 structure function also unitarizes and becomes linearly proportional to ln s. We also discuss possible applications of the developed technique to diffraction.

Figures (6)

• Figure 1: An example of the pomeron "fan" diagram.
• Figure 2: Dipole evolution in the deep inelastic scattering process as pictured in Ref.[1]. The incoming virtual photon develops a system of color dipoles, each of which rescatters on the nucleus (only two are shown).
• Figure 3: Plot of partial sums ($S_n$) of the series of Eq. (\ref{['psol']}) as functions of $P_1$, keeping $a=0.3$ for $n=1, \ldots ,12$. The thick line formed by the partial sums corresponds to the true value of ${\tilde{N}} (k,Y)$. The straight line represents the single BFKL pomeron exchange contribution.
• Figure 4: Plot of the qualitative behavior of the forward $q \overline{q}$ pair scattering amplitude on a nucleus, $N (x_\perp , Y)$ , as a function of $x_\perp Q_s (Y)$ (one BFKL pomeron exchange contribution). At small values of $x_\perp Q_s$ the structure function is linear in $x_\perp Q_s$, reproducing BFKL pomeron. As energy increases the forward amplitude $N$ saturates to a constant.
• Figure 5: Quasi--elastic deep inelastic scattering as pictured in [25].