On the 'toy model" in the Reggeon field theory

Abstract

The Reggeon field theory with zero transverse dimensions is studied in the Hamiltonian formulation for both sub-and supercritical pomeron. Mathematical aspects of the model, in particular the scalar products in the space of quantum states, are discussed. Relation to reaction-diffusion processes is derived in absence of pomeron merging. Numerical calculations for different parameters of the models, $α(0)-1=μ$ and the triple pomeron coupling constant $λ$, 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 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. A perturbative treatment is proposed which may be useful for more realistic models.