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.

arXiv comment22 pages, 8 figures, References added

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Cited by in corpus (22)

• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• Boundary conditions in the QCD nucleus-nucleus scattering problem
• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
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• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• All-loop calculation of the Reggeon field theory amplitudes via stochastic model
• Finite nuclei in the reggeon "toy" model
• On asymptotic solutions of RFT in zero transverse dimensions
• Loops in the Reggeon model for hA scattering
• On the one-dimensional reggeon model: eigenvalues of the Hamiltonian and the propagator
• Local one-dimensional reggeon model of the interaction of pomerons and odderons
• High energy scattering in Einstein-Cartan gravity
• On QCD RFT corrections to the propagator of reggeized gluons
• PT Symmetry and Hermithean Hamiltonian in the Local Supercritical Pomeron Model
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Dipole-dipole scattering amplitude in CGC approach
• Hadron-nucleus scattering in the local reggeon model with pomeron loops for realistic nuclei
• High energy QCD Lipatov's effective action in Euclidean space
• PT Symmetry and Renormalization in a Pomeron Model
• Local one-dimensional reggeon model of the interaction of several pomerons
• Four-pomeron vertex
• Structure Functions and Low-x -- Working Group Summary