Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

TL;DR

This paper explores toy models of interacting Pomerons in zero transverse dimensions, solving for quantum eigenstates and analyzing the impact of loop contributions on scattering amplitudes.

Contribution

It provides numerical solutions for eigenvalues and eigenfunctions, and compares models with and without quaternary Pomeron vertices, highlighting loop effects.

Findings

Loops significantly affect scattering amplitudes at various parameters.

Quantum solutions for the models are obtained and analyzed.

Differences between models with and without quaternary vertices are discussed.

Abstract

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.