Renormalization group equation, the naturalness problem, and the understanding of the Higgs mass term

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 Mt = 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 Mt ≤ 170.7 GeV.

Thermally modified sterile neutrino portal dark matter and gravitational waves from phase transition: the freeze-in case

“…With the gauge invariant approach by taking into account the tadpole contributions to the Higgs two-point green's function [51][52][53], the φ introduced here can be related with the fine-tuning of the Higgs, the quadratic corrections from the hidden scalar singlet is given by,…”

Comment on “Bare Higgs mass at Planck scale”

“…The standard model (SM) Higgs-like particle of mass 125 GeV recently discovered at the LHC [1,2] has resulted in a revival of interest in the old Veltman observation [3] that it is possible to arrange the cancellation of the quadratic divergence in the Higgs mass by imposing a certain relation upon the coupling constants of the theory [4][5][6][7][8]. In the notation of Ref.…”

“…Therefore the disagreements I have indicated above will not have much impact on the thrust of the arguments presented in Refs. [4][5][6][7][8], although it may well change the scale at which the total quadratic divergence reaches zero by an appreciable amount. For possible future applications it is as well to clarify which of the two calculations discussed here is correct.…”

Dimensional Regularization is Generic

“…Finally, we mention the works [19,20,21,22,23,24] where interesting physical issues related to quadratic divergences are analyzed from various points of view. · º¾ ¹½ º¾ ¹¾…”