Naturalness and theoretical constraints on the Higgs boson mass

TL;DR

This paper explores the regularization dependence of quadratic divergences in the Standard Model, proposing a symmetry-based approach to eliminate fine-tuning and derive bounds on the Higgs boson mass.

Contribution

It introduces a symmetry requirement based on scale symmetry breaking to fix the quadratic divergence coefficient, addressing naturalness and fine-tuning issues in the Higgs sector.

Findings

Quadratic divergences are regularization dependent and can be fixed by symmetry.

The proposed approach constrains the Higgs mass in terms of quantum corrections.

Including quadratic divergences implies large corrections to match experimental Higgs mass.

Abstract

Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of $\delta m^2/m^2_H$ (where $m_H$ is the renormalized Higgs mass and $\delta m^2$ is the 1-loop Higgs mass correction). Whereas $\delta m^2/m^2_H<1$ (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands $\delta m^2/m^2_H$ arbitrarily large to reach that experimental value.