# RG Equations and High Energy Behaviour in Non-Renormalizable Theories

## TL;DR

This paper develops a generalized renormalization group approach for non-renormalizable theories, demonstrating the existence of Landau poles at high energies in phi^4_D models across multiple dimensions.

## Contribution

It introduces a novel RG equation applicable to non-renormalizable theories, providing solutions that sum leading logarithms and revealing high-energy behavior.

## Key findings

- Derivation of a generalized RG equation for non-renormalizable theories
- Identification of Landau poles at high energy in phi^4_D models
- Applicability of the method to other 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 whether it is renormalizable or not. As a playground we take the phi^4_D 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 phi^4_D theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories.