Naturalness and Renormalization Group in 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.