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, $\alpha (0)-1=\mu$ and the triple pomeron coupling constant $\lambda$, 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 $\lambda /\mu$ the higher are rapidities $y$ at which this fall starts, so that at small values of $\lambda$ it begins at asymptotically high rapidities (for $\lambda /\mu <1/4$ the fall is noticeable only at $\mu y>100$). No visible singularity is seen for the critical pomeron. A perturbative treatment is proposed which may be useful for more realistic models.

22 pages, 8 figures, References added

References in corpus (1)

• Solution for the BFKL Pomeron Calculus in zero transverse dimensions

Cited by in corpus (11)

• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
• Langevin equation in effective theory of interacting QCD pomerons in the limit of large $N_c$
• Finite nuclei in the reggeon "toy" model
• Loops in the Reggeon model for hA scattering
• Dipole-dipole scattering amplitude in CGC approach
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Hadron-nucleus scattering in the local reggeon model with pomeron loops for realistic nuclei
• PT Symmetry and Renormalization in a Pomeron Model
• Structure Functions and Low-x -- Working Group Summary
• Local one-dimensional reggeon model of the interaction of several pomerons
• Four-pomeron vertex