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The Odderon in Quantum Chromodynamics

Carlo Ewerz

TL;DR

The Odderon addresses high-energy QCD exchange with negative C-parity and is rooted in Regge theory, now treated in perturbative BKP and nonperturbative approaches. The perturbative Odderon comprises three reggeized gluons whose dynamics are exactly solvable in certain limits and reveal an underlying integrable structure tied to SL(2,C) symmetry; notable solutions (JW and BLV) yield intercepts near or at unity, with BLV explicitly at α_O = 1 and JW close to 0.96 for typical α_s. Unitarity in the perturbative regime is addressed via the generalized LLLA (GLLA) framework, including N-reggeon states and Pomeron–Odderon–Odderon vertices, while nonperturbative QCD provides complementary pictures through Regge phenomenology, nonperturbative propagators, and stochastic vacuum models. Phenomenologically, Odderon effects are explored in pp/p̄p elastic scattering, exclusive diffractive meson production in ep and γγ processes, and interference-based observables; although data are currently inconclusive, several channels (e.g., diffractive J/ψ at HERA, double-diffractive meson production, and photon-photon processes at future colliders) hold promise for unambiguous Odderon discovery and spectral characterization.

Abstract

The Odderon is the leading exchange in hadronic scattering processes at high energies in which negative charge conjugation and parity quantum numbers are transferred in the t-channel. We review the origin of the Odderon in Regge theory, its status in perturbative and nonperturbative Quantum Chromodynamics, as well as its phenomenology.

The Odderon in Quantum Chromodynamics

TL;DR

The Odderon addresses high-energy QCD exchange with negative C-parity and is rooted in Regge theory, now treated in perturbative BKP and nonperturbative approaches. The perturbative Odderon comprises three reggeized gluons whose dynamics are exactly solvable in certain limits and reveal an underlying integrable structure tied to SL(2,C) symmetry; notable solutions (JW and BLV) yield intercepts near or at unity, with BLV explicitly at α_O = 1 and JW close to 0.96 for typical α_s. Unitarity in the perturbative regime is addressed via the generalized LLLA (GLLA) framework, including N-reggeon states and Pomeron–Odderon–Odderon vertices, while nonperturbative QCD provides complementary pictures through Regge phenomenology, nonperturbative propagators, and stochastic vacuum models. Phenomenologically, Odderon effects are explored in pp/p̄p elastic scattering, exclusive diffractive meson production in ep and γγ processes, and interference-based observables; although data are currently inconclusive, several channels (e.g., diffractive J/ψ at HERA, double-diffractive meson production, and photon-photon processes at future colliders) hold promise for unambiguous Odderon discovery and spectral characterization.

Abstract

The Odderon is the leading exchange in hadronic scattering processes at high energies in which negative charge conjugation and parity quantum numbers are transferred in the t-channel. We review the origin of the Odderon in Regge theory, its status in perturbative and nonperturbative Quantum Chromodynamics, as well as its phenomenology.

Paper Structure

This paper contains 44 sections, 271 equations, 37 figures.

Table of Contents

  1. Introduction
  2. Pomeron and Odderon in Regge Theory
  3. Regge Theory and the Pomeron
  4. Crossing and the Odderon
  5. Asymptotic Theorems and the Odderon
  6. The Maximal Odderon
  7. Theoretical Aspects of the Odderon in QCD
  8. High Energy Scattering in Perturbative QCD and the BFKL Pomeron
  9. The BFKL Equation
  10. Conformal Invariance of the BFKL Equation
  11. Solutions of the BFKL Equation in Impact Parameter Space
  12. Reggeization of the Gluon
  13. Applicability of the BFKL Pomeron
  14. The Odderon in Perturbative QCD
  15. The Bartels-Kwieciński-Praszałowicz Equation
  16. ...and 29 more sections

Figures (37)

  • Figure 1: Real gluon emissions from the $t$-channel gluon
  • Figure 2: Factorization of the perturbative Pomeron amplitude in the high energy limit
  • Figure 3: Diffusion of transverse momenta in the BFKL Pomeron
  • Figure 4: Transition from cigar--type evolution to tunneling--type evolution, figure from Ciafaloni:2002xk
  • Figure 5: Factorization of the perturbative Odderon amplitude in the high energy limit
  • ...and 32 more figures