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Pomeron Vertices in Perturbative QCD in Diffractive Scattering

J. Bartels, M. Braun, G. P. Vacca

TL;DR

The paper analyzes momentum-space diffractive vertices in perturbative QCD, clarifying how the standard triple Pomeron vertex V and the diffractive version Z relate, and then extends the framework to the Pomeron–Odderon–Odderon channel. By working in the large-$N_c$ limit and employing $D_4$, $D_6$, and the universal $G$-function formalism, it derives explicit diffractive vertices for both PPP and POO, and reveals their symmetry structures. The results illuminate how high-mass diffraction is described within the reggeon framework and how diffractive vertices interface with BK evolution, showing that the BK kernel captures only part of the two-Pomeron ladder contributions. The work also establishes the infrared finiteness and conformal properties of the diffractive vertices, providing a consistent tool for diffractive cross sections in pQCD.

Abstract

We analyse the momentum space triple Pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross-sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyse the relation between these two versions. We discuss some implications for the BK-equation. In the second part of our paper we extend this analysis to the Pomeron-Odderon-Odderon vertex.

Pomeron Vertices in Perturbative QCD in Diffractive Scattering

TL;DR

The paper analyzes momentum-space diffractive vertices in perturbative QCD, clarifying how the standard triple Pomeron vertex V and the diffractive version Z relate, and then extends the framework to the Pomeron–Odderon–Odderon channel. By working in the large- limit and employing , , and the universal -function formalism, it derives explicit diffractive vertices for both PPP and POO, and reveals their symmetry structures. The results illuminate how high-mass diffraction is described within the reggeon framework and how diffractive vertices interface with BK evolution, showing that the BK kernel captures only part of the two-Pomeron ladder contributions. The work also establishes the infrared finiteness and conformal properties of the diffractive vertices, providing a consistent tool for diffractive cross sections in pQCD.

Abstract

We analyse the momentum space triple Pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross-sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyse the relation between these two versions. We discuss some implications for the BK-equation. In the second part of our paper we extend this analysis to the Pomeron-Odderon-Odderon vertex.

Paper Structure

This paper contains 14 sections, 218 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Diffractive vertex for the splitting P$\to$ PP
  3. Definitions
  4. The explicit form of the diffractive triple Pomeron vertex
  5. Diffractive vertex for the splitting P$\to$ OO
  6. Definitions
  7. The explicit form of the diffractive POO vertex
  8. The symmetry structure of $X$ and the final diffractive vertex
  9. Conclusions
  10. Acknowledgements
  11. Appendix 1. Terms with $\omega$'s in the vertex PPP
  12. Appendix 2. Useful formulas for the POO diffractive vertex
  13. Action of $U_0$ on different terms in $D_6^R$
  14. Terms with $\omega$'s

Figures (5)

  • Figure 1: Decomposition for $D_4=D_4^R+D_4^I$.
  • Figure 2: Double Pomeron exchange ($G_2$ is the BFKL Pomeron Green's function).
  • Figure 3: (a) Graphical illustration of the definition of $D_4$; (b) the same equation after color projection and large $N_c$ limit.
  • Figure 4: Defining equation for $D_4^I$.
  • Figure 5: Equation for $D_6$.