Higgs mass implications on the stability of the electroweak vacuum

Abstract: We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124--126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around $10^{11}$ GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflation, which depends critically on the precise values of the Higgs and top masses. A Higgs mass in the range 124--126 GeV is compatible with very high values of the reheating temperature, without conflict with mechanisms of baryogenesis such as leptogenesis. We derive an upper bound on the mass of heavy right-handed neutrinos by requiring that their Yukawa couplings do not destabilize the Higgs potential.

• The paper demonstrates that a 124–126 GeV Higgs mass leads to a metastable electroweak vacuum, with potential instability around 10¹¹ GeV yet a decay time far exceeding the Universe’s age.
• The paper shows that precise measurements of the Higgs and top quark masses critically determine stability bounds and influence thermal parameters like the reheating temperature post-inflation.
• The paper employs renormalization group evolution—including effects from heavy right-handed neutrinos—to impose constraints on new physics scenarios beyond the Standard Model.

Higgs Mass Implications on the Stability of the Electroweak Vacuum

The research paper investigates the implications of recent experimental observations on the Higgs boson mass for the stability of the electroweak vacuum within the framework of the Standard Model (SM). The study takes into account the Higgs mass range indicated by the Large Hadron Collider (LHC) experiments and analyzes the theoretical bounds for vacuum stability, instability, and metastability, derived through the renormalization group (RG) evolution of the Higgs quartic coupling.

Overview of the Main Findings

The authors focus on Higgs mass values in the range of 124--126 GeV, incorporating recent results obtained from the ATLAS and CMS experiments. They explore the electroweak SM vacuum's stability under the hypothesis that these conditions persist up to the Planck scale. Emphasizing the interplay between the Higgs mass, top quark mass, and strong coupling, the paper deduces several significant conclusions:

1. Instability and Lifetime: The Higgs potential could experience an instability near energy scales around $10^{11}$ GeV. However, such an instability implies a lifetime for the electroweak vacuum that is considerably longer than the current age of the Universe, suggesting a metastable state.
2. Dependence on Higgs and Top Masses: Stability bounds and potential implications for early Universe conditions, such as reheating temperature after inflation, depend critically on precise measurements of Higgs and top masses.
3. Constraints from Metastability: For certain parameter ranges, the SM vacuum may be meta-stable but still consistent with the lifetime of the Universe, providing constraints on the scale of possible new physics or extensions, like heavy right-handed neutrinos affecting Yukawa couplings.

Practical and Theoretical Implications

The study's theoretical implications include refining understanding of the stability limits at extreme energy scales, critical for informing models of new physics beyond the SM. Practically, insights about constraints on the reheating temperature inform cosmological scenarios like leptogenesis, critical for explaining baryon asymmetry in the Universe:

• Thermal Constraints: An important result is the derived upper bound on the reheating temperature post-inflation, which is consequential for baryogenesis mechanisms. The Higgs and top masses directly affect this bound, influencing viable models for early Universe dynamics.
• Heavy Neutrino Contributions: The analysis extends to incorporating potential contributions from heavy right-handed neutrinos within the seesaw mechanism. The RG evolution of the Higgs quartic coupling is affected by the Yukawa couplings of these neutrinos, introducing meaningful constraints on their masses.

Future Prospects and Developments

The paper highlights avenues for future research stemming from improved experimental precision. Enhanced measurements of Higgs and top quark masses at the LHC will sharpen the theoretical bounds on vacuum stability, potentially ruling out or constraining alternative new physics scenarios.

Furthermore, the ongoing investigation of vacuum stability provides a nuanced understanding that may impact high-energy physics theories and cosmology, particularly regarding the Universe's evolution immediately after the Big Bang.

In conclusion, this study positions itself at the intersection of particle physics and cosmology, offering critical insights into the complex landscape of the electroweak vacuum stability contingent upon experimental and theoretical advancements.