Higgs boson and Top quark masses as tests of Electroweak Vacuum Stability (1209.0393v2)

Abstract: The measurements of the Higgs boson and top quark masses can be used to extrapolate the Standard Model Higgs potential at energies up to the Planck scale. Adopting a NNLO renormalization procedure, we: i) find that electroweak vacuum stability is at present allowed, discuss the associated theoretical and experimental errors and the prospects for its future tests; ii) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the Planck scale, which is a stable configuration that might have been relevant for primordial inflation; iii) derive a conservative upper bound on type I seesaw right-handed neutrino masses, following from the requirement of electroweak vacuum stability.

• The paper demonstrates that electroweak vacuum stability is feasible within current experimental ranges by analyzing the Higgs quartic coupling's high-energy behavior.
• It identifies conditions for a shallow false minimum near the Planck scale, suggesting a possible role in triggering primordial inflation.
• By applying type I seesaw mechanisms, the research constrains right-handed neutrino masses, linking them to precise Higgs and top quark measurements.

Electroweak Vacuum Stability: Insights from Higgs Boson and Top Quark Masses

The paper scrutinizes the implications of the recently pinpointed Higgs boson and top quark masses for electroweak vacuum stability, extrapolating the Standard Model (SM) Higgs potential up to the Planck scale using a NNLO renormalization scheme. It serves as a cohesive synthesis of experimental and theoretical progress, endeavoring to illuminate the stability landscape of our universe within the framework of the SM.

Main Findings and Methodological Framework

The primary objective is threefold: first, to ascertain whether electroweak vacuum stability is feasible within the current experimental constraints; second, to delineate the conditions under which a shallow false minimum might occur below the Planck scale—a conjecture associated with primordial inflation; and third, to impose constraints on the type I seesaw right-handed neutrino masses based on vacuum stability requirements.

1. Electroweak Stability Analysis: The research yields that electroweak vacuum stability is conceivable within the experimentally determined ranges of Higgs and top quark masses, albeit with notable theoretical and experimental uncertainties. The paper accentuates the sensitivity of the Higgs quartic coupling's behavior at high energies to the masses of these particles. The authors identify a demarcation line indicating the transition from stability to metastability in the top mass vs. Higgs mass space.
2. Shallow False Minimum Conditions: The examination of the Higgs potential's high-energy behavior reveals conditions for an intriguing shallow false minimum near the Planck scale. The authors conjecture that such a configuration might have played a role in inflationary scenarios. For these configurations, the Higgs quartic coupling becomes minute or negative within a precise parameter window, potentially triggering inflation.
3. Seesaw Mechanism Constraints: By integrating the effects of a type I seesaw mechanism, the paper constrains the mass of a right-handed neutrino such that the SM retains its stability, which is primarily dependent on the top quark mass. The bound on neutrino masses is sensitive to the Higgs and top quark masses, providing a pathway to potentially bridge observational astroparticle physics with high-energy phenomenology.

Theoretical and Practical Implications

The ramifications of this work are manifold:

• The vacuum stability bound serves as a pivotal criterion for theorists constructing new physics models that extend the SM. Any Beyond the Standard Model (BSM) framework should align with these stability criteria unless it explicitly alters the Higgs sector.
• The notion of a shallow false minimum impacting cosmology calls for a deeper exploration into the cosmological role of the Higgs field, especially concerning inflationary paradigms.
• Constraining seesaw models through vacuum stability considerations bridges the gap between particle physics and cosmological observations, highlighting the relevance of neutrino physics in grander cosmological themes.

Future Prospects

This research underscores future directions for both experimental and theoretical pursuits. Experimentally, a precise determination of the Higgs boson, top quark masses, and the strong coupling constant is crucial for reducing uncertainties in vacuum stability assessments. Theoretically, understanding vacuum stability could stimulate innovative approaches in particle physics, cosmology, and quantum gravity.

In sum, this paper enriches our understanding of electroweak vacuum stability within the SM paradigm, integrating key experimental insights with robust theoretical analysis, and setting the stage for future explorations into the frontiers of particle physics and cosmology.