Diffractive Dissociation Including Multiple Pomeron Exchanges in High Parton Density QCD

TL;DR

The paper tackles single diffractive dissociation in deep inelastic scattering at small x by deriving a nonlinear evolution equation that resums multiple BFKL pomeron exchanges within Mueller's dipole formalism, and confirms consistency with AGK cutting rules. It introduces the diffractive cross section $N^D(x_{01}, b, Y, Y_0)$ and its coupling to the elastic amplitude $N_0$, providing an explicit evolution equation (and its differential form) that accounts for rapidity-gap constraints. A toy-model analysis reveals a non-monotonic behavior: the fixed-gap diffractive cross section grows with the gap at moderate energies but develops a maximum at large gaps due to saturation, with the asymptotic limit $N^D \to 1$ signaling a black disk. The results propose diffractive DIS cross sections as a sensitive observable for nonlinear QCD dynamics and saturation, while noting the need for numerical solutions and the possible role of pomeron loops in real nuclei.

Abstract

We derive an evolution equation describing the high energy behavior of the cross section for the single diffractive dissociation in deep inelastic scattering on a hadron or a nucleus. The evolution equation resums multiple BFKL pomeron exchanges contributing to the cross section of the events with large rapidity gaps. Analyzing the properties of an approximate solution of the proposed equation we point out that at very high energies there is a possibility that for a fixed center of mass energy the cross section will reach a local maximum at a certain intermediate size of the rapidity gap, or, equivalently, at some non-zero value of the invariant mass of the produced particles.

Figures (9)

• Figure 1: An example of the pomeron "fan" diagram, which were considered in deriving (\ref{['eqN']}).
• Figure 2: Single diffractive dissociation process considered in the paper. The interaction between the target and virtual photon is represented schematically by an exchange of a color singlet object.
• Figure 3: Traditional description of single diffractive dissociation. Dash-dotted line represents the final state.
• Figure 4: A diagram contributing to the diffractive dissociation with rapidity gap $Y_0$ as considered in the text.
• Figure 5: An example of elastic scattering of the quark--antiquark pair on the nucleus as pictured in the text.