Bounds on Higgs And Top Quark Masses From The Other Degenerate Vacua Near The Planck Scale With Gravitational Contributions

TL;DR

This paper investigates how gravitational effects influence the Standard Model couplings and uses these insights to constrain the Higgs and top quark masses based on the existence of degenerate vacua near the Planck scale.

Contribution

It provides a detailed calculation of gravitational contributions to SM couplings using a gauge-preserving regularization scheme and explores their implications for Higgs and top quark mass bounds.

Findings

Current Higgs and top masses do not support degenerate vacua at the Planck scale.

Degenerate vacua at the Planck scale suggest Higgs mass around 130 GeV and top mass around 174 GeV.

Gravitational contributions depend on gauge-fixing parameters, affecting the analysis.

Abstract

Based on the weak coupling expansion of gravity, we calculate the gravitational contributions to yukawa coupling, scalar quartic coupling as well as gauge couplings with general Landau-DeWitt gauge-fixing choice and a gauge preserving (of SM gauge group) cut off regularization scheme. We find that the results depend on the Landau-DeWitt gauge-fixing parameter. Based on the two loop RGE of SM couplings with one loop full gravitational contributions in harmonic gauge, we study the constraints on the higgs and top quark mass from the requirement of existing the other degenerate vacua at the Planck-dominated region. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the higgs and top mass to lie at approximately 130 and 174 GeV, respectively.