The origin of a high-energy scale in the Pomeron calculus

The Gribov-Reggeon calculus, whose perturbative expansion is expected to converge at low energy, is known to give rise to critical phenomena at ultra-high energies. The aim of this paper is to investigate the transition between these two regimes and to determine the scale with which this transition happens. This is done by solving exactly the renormalization group equation in a model theory. The propagator shows a singularity whose position determines the scale in question. The dynamical origin of this scale — whose evaluation situates it beyond present machine energies — is discussed, and so the dual relation between the perturbative and the critical expansions.