RG equations and high energy behaviour in non-renormalizable theories

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 ϕD4 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 ϕD4 theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories. Keywords: Renormalization, UV divergences, Non-renormalizable interactions

Abstract licence: CC BY

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