RG equations and high energy behaviour in non-renormalizable theories

Abstract We suggest a novel view on non-renormalizable interactions. It is based on the usual BPHZ R -operation which is equally applicable to any local QFT independently of whether it is renormalizable or not. As a playground we take the ϕ D 4 theory in D dimensions for D = 4 , 6 , 8 , 10 and consider the four-point scattering amplitude on shell. We derive the generalized RG equation and find the solution valid for any D that sums up the leading logarithms in all orders of PT in full analogy with the renormalizable case. It is found that the scattering amplitude in the ϕ D 4 theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories.