High energy scattering in the Unitary Toy Model

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.