High energy scattering in the Unitary Toy Model

TL;DR

This paper advances the understanding of high energy collisions in the Unitary Toy Model by diagonalizing its Hamiltonian, resumming divergent series, and analyzing eigenvalues to gain insights relevant to QCD Pomeron calculus.

Contribution

It introduces a new diagonalization approach for the UTM Hamiltonian and develops resummation techniques for the divergent multi-Pomeron series, providing insights applicable to real QCD.

Findings

Identification of Hamiltonian spectrum with Pomeron intercepts

Successful resummation of divergent S-matrix series

Negative eigenvalues influence saturation dynamics

Abstract

We continue exploring the Unitary Toy Model (UTM) as a playground for high energy collisions in QCD. Our new approach is based on the diagonalization of the evolution Hamiltonian. Part of the spectrum can be identified with intercepts of dressed Pomerons. Analogously to QCD, a multi-Pomeron expansion of the $S$-matrix is badly divergent asymptotic series. Yet we succeeded to establish resummation procedures resulting in a well behaved $S$-matrix. In addition the Hamiltonian possesses negative eigenvalues, which dominate the approach of the $S$-matrix to saturation. We are hopeful that important lessons about BFKL-based Pomeron calculus could be taken from the toy world to real QCD.