Entropy in Toy Regge models

TL;DR

This paper explores the probabilistic interpretation of Toy Regge models with triple pomeron interactions, proposing alternative probability frameworks based on pomerons and analyzing their entropy behavior and potential observable effects.

Contribution

It introduces alternative probability definitions within Toy Regge models, contrasting them with traditional parton-based interpretations, and examines their entropy and observable implications.

Findings

Pomeron-based probabilities differ significantly from standard interpretations.

Entropy behavior varies, showing saturation or a rise and fall pattern.

Observable effects may appear in cross-section distributions.

Abstract

The probabilistic interpretation of the standard Regge-Gribov model with triple pomeron interactions is discussed. It is stated that introduction of probabilities within this model is not unique and depends on what is meant under the relevant substructures, The traditional interpretation in terms of partons (quarks and gluons) is shown to be external to the model, imported from the QCD, and actually referring to the single pomeron exchange without interactions. So this interpretation actually forgets the model as such. Alternative probabilities based on the pomerons as basic quantities within the model are discussed. Two different approaches are considered, based either on the pomerons in Fock's expansion of the wave function or on pomeron propagators in Feynman diagrams. These pomeron probabilities and entropy turn out to be very different from the mentioned standard ones in the purelyp obabilistic treatment. The entropy, in particular, either rises with the rapidity and saturates at a certain fixed value or first rises, reaches some maximum and goes down to zero afterwards. Possible observable manifestations of these probabilities and entropy are to be seen in the distributions of the cross-section in powers of the coupling constants to the participants. 23