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On the reggeon model with the pomeron and odderon: singularities with non-zero masses

M. A. Braun, E. M. Kuzminskii, M. I. Vyazovsky

TL;DR

The paper investigates the Regge-Gribov pomeron–odderon system in two transverse dimensions using a one-loop renormalization-group analysis with two mass-like parameters. It derives the RG flow, fixed points, and scaling functions, and studies the high-energy elastic amplitude, finding branch-point singularities near fixed points that signal non-physical phases when intercepts exceed unity. Among the fixed points, only the purely attractive point $g_c^{(3)}$ yields a physically acceptable scaling, with the leading high-energy behavior governed by single pomeron exchange, producing a cross-section growth compatible with the Froissart bound; odderon effects are subdominant or constrained. The results suggest that the odderon does not rescue the reggeon model in the supercritical regime and emphasize the need for beyond-one-loop or alternative approaches to fully resolve the high-energy regime in this framework.

Abstract

The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique in the single loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behaviour when the intercepts move from below to their critical values compatible with the Froissart limitation is studied. The singuarities in the form of non-trivial branch points indicating a phase transition are found in the vicinity of five fixed points found in the previous publication. Since new phases violate the projectile-target symmetry the model is found non-physical for the bare intercepts above their critical value.

On the reggeon model with the pomeron and odderon: singularities with non-zero masses

TL;DR

The paper investigates the Regge-Gribov pomeron–odderon system in two transverse dimensions using a one-loop renormalization-group analysis with two mass-like parameters. It derives the RG flow, fixed points, and scaling functions, and studies the high-energy elastic amplitude, finding branch-point singularities near fixed points that signal non-physical phases when intercepts exceed unity. Among the fixed points, only the purely attractive point yields a physically acceptable scaling, with the leading high-energy behavior governed by single pomeron exchange, producing a cross-section growth compatible with the Froissart bound; odderon effects are subdominant or constrained. The results suggest that the odderon does not rescue the reggeon model in the supercritical regime and emphasize the need for beyond-one-loop or alternative approaches to fully resolve the high-energy regime in this framework.

Abstract

The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique in the single loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behaviour when the intercepts move from below to their critical values compatible with the Froissart limitation is studied. The singuarities in the form of non-trivial branch points indicating a phase transition are found in the vicinity of five fixed points found in the previous publication. Since new phases violate the projectile-target symmetry the model is found non-physical for the bare intercepts above their critical value.

Paper Structure

This paper contains 21 sections, 341 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model. Renormalization and evolution
  3. Self-masses, anomalous dimensions and $\beta$-functions
  4. Self-masses and renormalization constants $Z$, $U$ and $T$
  5. Anomalous dimensions, $\beta$-functions and fixed points
  6. At the fixed point with small $\delta_1$
  7. Scaling
  8. Scaling functions at the fixed point
  9. Trajectories
  10. Small $\delta_2$
  11. Scaling functions
  12. Trajectories
  13. Elastic scattering amplitude
  14. The asymptotic
  15. At fixed point and with $D=2$
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Self masses for $\Gamma_1$ ($a+b$) and $\Gamma_2$ ($c$). Pomerons and odderons are shown by solid and dashed lines respectively.
  • Figure 2: Elastic amplitude with a given number of pomerons (solid lines) and odderons (dashed lines) exchanges.
  • Figure 3: Elastic amplitude when the Green function contains two disconnected parts.