Renormalization Group Equation for Weakly Power Counting Renormalizable Theories

TL;DR

This paper establishes a renormalization group equation for weak power counting renormalizable theories, ensuring their divergence structure remains consistent under scale changes, with implications for beyond Standard Model physics.

Contribution

It proves that WPC renormalizable theories maintain their divergence control under RG flow, even in complex symmetry-breaking frameworks.

Findings

RG equation preserves WPC condition

Finite counterterms absorb scale variations

Applicable to non-linear Stueckelberg-like models

Abstract

We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent amplitudes order by order in the loop expansion. Using as a toolbox the well-known SU(2) non linear sigma model, we prove that for such theories a renormalization group equation holds that does not violate the WPC condition: that is, the sliding of the scale $\mu$ for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by the WPC itself. We explore in some detail the consequences of this result; in particular, we prove that it holds in the framework of a recently introduced beyond the Standard Model scenario in which one considers non-linear St\"uckelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.