The Regge-Gribov model with odderons

TL;DR

This paper develops a Regge-Gribov model incorporating odderons, analyzing phase transitions and fixed points through numerical and renormalization group methods, revealing non-physical phases and asymptotic scattering behaviors.

Contribution

It introduces a novel Regge-Gribov model with odderons, studying its fixed points and phase transitions using advanced numerical and renormalization techniques.

Findings

No phase transition occurs in the zero transverse dimension model.

Five real fixed points with non-trivial branch points are identified.

Asymptotic behaviors of Green functions and scattering amplitudes are characterized.

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.