On Naturalness of Scalar Fields and Standard Model

TL;DR

This paper examines how different naturalness conditions affect the predicted scale of new physics and the Higgs boson mass in the Standard Model, emphasizing the importance of higher order corrections.

Contribution

It compares two naturalness conditions, showing that higher order corrections make the scalar field system more natural and refine Higgs mass constraints.

Findings

Veltman's condition is stable under higher order corrections.

Barbieri-Giudice condition is sensitive to higher order corrections.

Higher order corrections mitigate fine-tuning issues in the Standard Model.

Abstract

We discuss how naturalness predicts the scale of new physics. Two conditions on the scale are considered. The first is the more conservative condition due to Veltman (Acta Phys. Polon. B 12, 437 (1981)). It requires that radiative corrections to the electroweak mass scale would be reasonably small. The second is the condition due to Barbieri and Giudice (Nucl. Phys. B 306, 63 (1988)), which is more popular lately. It requires that physical mass scale would not be oversensitive to the values of the input parameters. We show here that the above two conditions behave differently if higher order corrections are taken into account. Veltman's condition is robust (insensitive to higher order corrections), while Barbieri-Giudice condition changes qualitatively. We conclude that higher order perturbative corrections take care of the fine tuning problem, and, in this respect, scalar field is a natural system. We apply the Barbieri-Giudice condition with higher order corrections taken into account to the Standard Model, and obtain new restrictions on the Higgs boson mass.