Renormalization group for multiparticle production in (2+1) dimensions around the threshold

Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in final state. We develop a technique based on renormalization group for summing up leading logarithms and apply it to the \phi^4 models with and without symmetry breaking and to the O(N) \phi^4 theory