On the dT=0 toy model in reggeon field theory

Abstract

Reggeon field theory with zero transverse dimensions is critically reanalyzed in the Hamiltonian formulation for both a sub- and a supercritical pomeron. Different mathematical aspects of the model, starting from the scalar products in the space of quantum states, are discussed. The probabilistic picture is addressed in the absence of pomeron merging. The issue of the large loop approximation is discussed in terms of the Hamiltonian evolution and its relation to the probabilistic picture recalled. A perturbative treatment, based on the PT symmetry of the model, is proposed that may be useful for more realistic models. Finally, we present numerical calculations for the various parameters of the models, α(0)-1=μ and the triple-pomeron coupling constant λ, which help one to understand some mathematical aspects and the different approximation regimes. They show that the triple-pomeron interaction always makes amplitudes fall with rapidity, irrespective of the value of the intercept. The smaller the values of the ratio λ/μ, the higher are the rapidities y at which this fall starts, so that at small values of λ it begins at asymptotically high rapidities (for λ/μ<1/4 the fall is noticeable only at μy>100). No visible singularity is seen for the critical pomeron.