Naturalness and Renormalization Group in the Standard Model

TL;DR

This paper formalizes the concept of naturalness in quantum field theories, compares different renormalization schemes, and explores implications for the Standard Model's naturalness and potential schemes.

Contribution

It introduces a formal naturalness criterion, demonstrates scheme-dependent naturalness in $\

Findings

A theory can be natural in the MS scheme but unnatural in the Gell-Mann--Low scheme.

The paper discusses the potential application of the Gell-Mann--Low scheme to the Standard Model.

Abstract

I define a naturalness criterion formalizing the intuitive notion of naturalness discussed in the literature. After that, using $\phi^4$ as an example, I demonstrate that a theory may be natural in the $MS$-scheme and, at the same time, unnatural in the Gell-Mann--Low scheme. Finally, I discuss the prospects of using a version of the Gell-Mann--Low scheme in the Standard Model.