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QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All

T. Altinoluk, C. Contreras, A. Kovner, E. Levin, M. Lublinsky, A. Shulkin

TL;DR

This work establishes a direct mapping between KLWMIJ high-energy QCD evolution and Reggeon Field Theory in the dilute-projectile limit, by constructing a gauge-invariant Reggeon basis consisting of the Pomeron, Odderon, and quadrupole-derived reggeons B and C (plus higher-point operators). It derives the RFT Hamiltonian as a sum of Reggeon sectors $H_{RFT}=H_P+H_O+H_B+H_C$, including explicit P^ abla,O^ abla,B^ abla,C^ abla conjugates and their evolution, and shows how Bartels’ triple-Pomeron vertex and BKP-type dynamics emerge naturally in this framework. The authors provide a systematic procedure to disentangle irreducible and reggeized parts of multi-point correlators, reproduce known reggeization results, and extend to higher-point functions with a clear algorithm. They also discuss how 1/N_c corrections reintroduce Reggeon merging vertices and outline potential extensions to Pomeron loops and the JIMWLK regime via dual Reggeons. Overall, the paper offers a rigorous, unambiguous bridge between CGC-based evolution and Reggeon field theory with concrete operator realizations and evolution equations for a controlled set of Reggeons.

Abstract

We show explicitly how the high energy QCD evolution generated by the KLWMIJ Hamiltonian can be cast in the form of the QCD Reggeon Field Theory. We show how to reduce the KLWMIJ Hamitonian to physical color singlet degrees of freedom. We suggest a natural way of defining the Pomeron and other Reggeons in the framework of the KLWMIJ evolution and derive the QCD Reggeon Field Theory Hamiltonian which includes several lowest Reggeon operators. This Hamiltonian generates evolution equations for all Reggeons in the case of dilute-dense scattering, including the nonlinear Balitsky-Kovchegov equation for the Pomeron. We also find explicit expressions for the Reggeon conjugate operators in terms of QCD operators, and derive their evolution equations. This provides a natural and unambiguous framework for reggeization procedure introduced in \cite{BW, BE}. The Bartels triple Pomeron vertex is inherited directly from the RFT Hamiltonian. For simplicity in the bulk of the paper we work in the large $N_c$ limit.

QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All

TL;DR

This work establishes a direct mapping between KLWMIJ high-energy QCD evolution and Reggeon Field Theory in the dilute-projectile limit, by constructing a gauge-invariant Reggeon basis consisting of the Pomeron, Odderon, and quadrupole-derived reggeons B and C (plus higher-point operators). It derives the RFT Hamiltonian as a sum of Reggeon sectors , including explicit P^ abla,O^ abla,B^ abla,C^ abla conjugates and their evolution, and shows how Bartels’ triple-Pomeron vertex and BKP-type dynamics emerge naturally in this framework. The authors provide a systematic procedure to disentangle irreducible and reggeized parts of multi-point correlators, reproduce known reggeization results, and extend to higher-point functions with a clear algorithm. They also discuss how 1/N_c corrections reintroduce Reggeon merging vertices and outline potential extensions to Pomeron loops and the JIMWLK regime via dual Reggeons. Overall, the paper offers a rigorous, unambiguous bridge between CGC-based evolution and Reggeon field theory with concrete operator realizations and evolution equations for a controlled set of Reggeons.

Abstract

We show explicitly how the high energy QCD evolution generated by the KLWMIJ Hamiltonian can be cast in the form of the QCD Reggeon Field Theory. We show how to reduce the KLWMIJ Hamitonian to physical color singlet degrees of freedom. We suggest a natural way of defining the Pomeron and other Reggeons in the framework of the KLWMIJ evolution and derive the QCD Reggeon Field Theory Hamiltonian which includes several lowest Reggeon operators. This Hamiltonian generates evolution equations for all Reggeons in the case of dilute-dense scattering, including the nonlinear Balitsky-Kovchegov equation for the Pomeron. We also find explicit expressions for the Reggeon conjugate operators in terms of QCD operators, and derive their evolution equations. This provides a natural and unambiguous framework for reggeization procedure introduced in \cite{BW, BE}. The Bartels triple Pomeron vertex is inherited directly from the RFT Hamiltonian. For simplicity in the bulk of the paper we work in the large limit.

Paper Structure

This paper contains 14 sections, 139 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The High Energy Evolution.
  3. Elements of Reggeon Calculus: the Pomeron and Other Reggeons.
  4. Elements of Reggeon Calculus: the Evolution and the Hamiltonian.
  5. The Conjugate Reggeons.
  6. Reggeization a la Bartels et.al.
  7. Operator Symmetrization and the Odd-point Functions.
  8. The Irreducible Four Point Function and The Conjugate Reggeons.
  9. Higher point functions.
  10. Discussion and Conclusions.
  11. Appendix
  12. The B-reggeon amended.
  13. The calculation of the conjugate B-reggeon.
  14. Symmetrization

Figures (3)

  • Figure 1: Triple Reggeon vertices derived from the KLWMIJ Hamiltonian
  • Figure 2: $D^2$ and $D^4$
  • Figure 3: $D^4_P$ and $D^4_B$