The Regge-Gribov model with odderons

TL;DR

The paper presents a Regge-Gribov model incorporating both pomerons and odderons with signature-conserving triple vertices, first analyzed in a zero-transverse-dimensions toy setting and then in two transverse dimensions using a one-loop renormalization-group framework. Five real fixed points emerge in the RG analysis, with only one, $g_c^{(3)}$, fully attractive; near $D=2$ the propagators acquire fractional exponents, and the elastic amplitude is dominated by single pomeron exchange with a subleading odderon contribution. The physical regime is constrained by projectile–target symmetry, and the high-energy behavior yields total cross-sections growing as $(\\ln s)^{1/6}$ (pomeron) and $(\\ln s)^{1/12}$ (odderon). The work highlights the robustness of the pomeron-dominated rise under odderon coupling, the necessity of higher-loop corrections, and the intricate fixed-point structure that governs reggeon interactions in this framework.

Abstract

The Regge-Gribov model describing interacting pomerons and odderons is proposed with triple reggeon vertices taking into account the negative signature of the odderon. Its simplified version with zero transverse dimensions is first considered. No phase transition occurs in this case at the intercept crossing unity. This simplified model is studied without more approximations by numerical techniques. The physically relevant model in the two-dimensional transverse space is then studied by the renormalization group method 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. Five real fixed points are found with singularities in the form of non-trivial branch points indicating a phase transition as the intercepts cross unity. The new phases, however, are not physical, since they violate the projectile-target symmetry. In the vicinity of fixed points the asymptotical behaviour of Green functions and elastic scattering amplitude is found under Glauber approximation for couplings to participants.

Figures (6)

• Figure 1: The solid curves show pomeron (left panel) and odderon (right panel) propagators as functions of rapidity for $\mu_1=1$, $\lambda=1/3$. The dashed curve in the left panel shows the pomeron propagator in absence of the odderon (only pomeron loops).
• Figure 2: The pomeron ground state energies $E$ vs their theoretical values without odderon $E_P$ for different $\rho$ in the model with odderon.
• Figure 3: Self masses for $\Gamma_1$ ($a+b$) and $\Gamma_2$ ($c$). Pomerons and odderons are shown by solid and dashed lines, respectively.
• Figure 4: Diagrams for $\Gamma^{10,20}$ ($a+b$), $\Gamma^{10,02}$ ($c+d$) and $\Gamma^{01,11}$ ($e+f$). Inverse diagrams for $\Gamma^{10,20}$ and $\Gamma^{10,02}$ are identical. For $\Gamma^{01,11}$ inverse diagrams are different and shown as ($e'$) and ($f'$). Pomerons and odderons are shown by solid and dashed lines, respectively.
• Figure 5: Elasic amplitude with a given number of pomerons (solid lines) and odderons (dashed lines) exchanges.