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Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

Alex Kovner, Michael Lublinsky

TL;DR

This work establishes a precise mapping between the KLWMIJ/JIMWLK evolution in high-energy QCD and a quantum Reggeon field theory, with the Reggeon field identified as the unitary Wilson line R and the t-channel exchanges encoded in universal eigenfunctions G_q[R]. It uncovers a rich spectrum in the one- and two-particle sectors, including the reggeized gluon, several CP-even Pomerons beyond the standard BFKL Pomeron, and multiple CP-odd Odderons, whose intercepts scale with representations and 1/N corrections, revealing new unitarization corrections beyond BKP. The paper also analyzes dipole scattering within this framework, showing how leading BFKL behavior arises perturbatively while higher Reggeon contributions appear at higher orders and are suppressed in dilute targets, highlighting the role of multiple scatterings in unitarization. It discusses how the partonic approximation relates to BFKL/BKP and the need for incorporating Pomeron loops to restore full t-channel unitarity, outlining open questions about symmetries, conformal structure, and nonperturbative extensions. Overall, the work provides a concrete bridge between perturbative Reggeon theory and the JIMWLK/KLWMIJ formalism, offering new insights into high-energy QCD dynamics and unitarization mechanisms.

Abstract

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Studying the single $s$ - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ($s$ - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$ limit are $1+ω_P=1+2ω$ where $1+ω$ is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least $1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron we find $ω_{[27,27]}=2ω+O(1/N)>2ω$. We also find three charge conjugation odd exchanges, one of which is the unit intercept Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than unity. We explain in what sense our calculation goes beyond the standard BFKL/BKP calculation. We make additional comments and discuss open questions in our approach.

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

TL;DR

This work establishes a precise mapping between the KLWMIJ/JIMWLK evolution in high-energy QCD and a quantum Reggeon field theory, with the Reggeon field identified as the unitary Wilson line R and the t-channel exchanges encoded in universal eigenfunctions G_q[R]. It uncovers a rich spectrum in the one- and two-particle sectors, including the reggeized gluon, several CP-even Pomerons beyond the standard BFKL Pomeron, and multiple CP-odd Odderons, whose intercepts scale with representations and 1/N corrections, revealing new unitarization corrections beyond BKP. The paper also analyzes dipole scattering within this framework, showing how leading BFKL behavior arises perturbatively while higher Reggeon contributions appear at higher orders and are suppressed in dilute targets, highlighting the role of multiple scatterings in unitarization. It discusses how the partonic approximation relates to BFKL/BKP and the need for incorporating Pomeron loops to restore full t-channel unitarity, outlining open questions about symmetries, conformal structure, and nonperturbative extensions. Overall, the work provides a concrete bridge between perturbative Reggeon theory and the JIMWLK/KLWMIJ formalism, offering new insights into high-energy QCD dynamics and unitarization mechanisms.

Abstract

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of - channel gluons. The eigenstates have a natural interpretation in terms of the - channel exchanges. Studying the single - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ( - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large limit are where is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least relative to the double BFKL Pomeron exchange. For the Pomeron we find . We also find three charge conjugation odd exchanges, one of which is the unit intercept Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than unity. We explain in what sense our calculation goes beyond the standard BFKL/BKP calculation. We make additional comments and discuss open questions in our approach.

Paper Structure

This paper contains 17 sections, 191 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. High energy scattering: the general setup
  3. Correspondence with the standard RFT language.
  4. Reggeons in the dipole model
  5. Reggeons in QCD
  6. The Hamiltonian
  7. One-particle state: reggeized gluon and other Reggeons
  8. Two-particle state
  9. Pomeron and family.
  10. Odderon and friends.
  11. Scattering of a gluonic dipole
  12. The perturbation.
  13. Partonic approximation versus BFKL/BKP
  14. Discussion
  15. Appendix: Evolution of $D^4$.
  16. ...and 2 more sections

Figures (5)

  • Figure 1: $t$-channel projection of Wilson lines.
  • Figure 2: $s$-channel projection of two Wilson lines.
  • Figure 3: The $t$-channel projection of two Wilson lines. Each one of the two $s$ - channel gluons exchanges a given color representation with the target. Additionally the two exchanges form an overall color singlet.
  • Figure 4: $t$-channel bound states of reggeized gluons.
  • Figure 5: The crossing matrix $C$