Probabilities in Toy Regge models with odderons

Abstract The possibility of a probabilistic interpretation is studied for the Regge–Gribov model in zero dimensional transverse world (“Toy”) with interacting pomerons and odderons. It is found that the old recipe (Bondarenko et al. in Eur Phys J C 50:593, 2007), which allowed to introduce such interpretation in the model without odderons, does not work once odderons are included. Starting from the physically reasonable probabilities it leads to a pathological field theory violating C -parity invariance. Vice versa, starting from an admissible field theory one comes to pathological probabilities, which not only violate C -invariance but also allow particles to be created from or annihilated into the vacuum. A method is proposed to introduce reasonable probabilities based directly on the Fock components of the wave function. Such probabilities manifest themselves in the multiplicity distributions of hadrons produced in high-energy collisions. The corresponding entropy grows with rapidity but saturates in the limit. It is found to be similar for $$C=\pm 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> processes.