RGE, the naturalness problem and the understanding of the Higgs mass term

TL;DR

This paper explores the naturalness problem of the Higgs mass using renormalization group equations and dimensional regularization, suggesting the problem may be due to rescaling effects rather than quadratic divergences, with implications for high-energy physics.

Contribution

It introduces a novel perspective on the naturalness problem by emphasizing rescaling effects over quadratic divergences and analyzes the Higgs mass behavior up to the Planck scale.

Findings

Higgs mass approaches zero at the UV scale in the RGE framework.

The naturalness problem may be due to rescaling effects, not quadratic divergences.

A tiny Higgs mass can exist at high energy scales when the top quark mass is below 170.7 GeV.

Abstract

The naturalness problem might be studied on the complex two dimensional plane with the technique of dimensional regularization(DREG). The Renormalization group equation(RGE) of the Higgs mass on the plane suggests the Higgs mass approaches zero at ultraviolate (UV) scale, the scale can be Planck scale when the top quark pole mass $M_{t}=168$ GeV. The real issue of the naturalness problem in the sense of Wilsonian renormalization group method is not about quadratic divergences but the rescaling effect. The Higgs mass can be considered to be one composed mass. All terms in the lagrangian in this scenario are marginal terms and no relevant terms are left, thus no rescaling effect to cause the naturalness problem anymore. RGE of the vacuum expectation value (VEV) in the Landau gauge up to two-loop order is studied. Scale-dependent behavior of the composed Higgs mass shows that we can have one tiny Higgs mass at high energy scale, even around the Planck scale, when $M_{t}\leq170.7$ GeV.