Investigating the near-criticality of the Higgs boson

Abstract: We extract from data the parameters of the Higgs potential, the top Yukawa coupling and the electroweak gauge couplings with full 2-loop NNLO precision, and we extrapolate the SM parameters up to large energies with full 3-loop NNLO RGE precision. Then we study the phase diagram of the Standard Model in terms of high-energy parameters, finding that the measured Higgs mass roughly corresponds to the minimum values of the Higgs quartic and top Yukawa and the maximum value of the gauge couplings allowed by vacuum metastability. We discuss various theoretical interpretations of the near-criticality of the Higgs mass.

• The paper uses full two-loop NNLO calculations to precisely measure the Higgs boson mass and extract Standard Model parameters, establishing its near-critical nature.
• It extrapolates these parameters to the Planck scale, showing that the quartic and Yukawa couplings align at boundaries indicative of a metastable vacuum state.
• The findings reveal that the Higgs boson occupies a metastable point near the phase transition threshold, offering crucial insights for probing physics beyond the Standard Model.

Investigating the Near-Criticality of the Higgs Boson

The paper "Investigating the near-criticality of the Higgs boson" explores an examination of the parameters defining the Higgs boson's potential under the framework of the Standard Model (SM). Focusing on the precision measurement of the Higgs boson mass, the authors offer insights into its position relative to stability boundaries suggesting its critical positioning.

Key Contributions and Findings

1. Precision Measurements: Utilizing data with full two-loop next-to-next-to-leading order (NNLO) accuracy for the Higgs potential and three-loop NNLO renormalization group equations (RGE), the authors extract the SM parameters. This meticulous approach calculates the Higgs quartic coupling, top Yukawa coupling, and electroweak gauge couplings to determine their stability and trends at high energies.
2. Phase Diagram and Near-Criticality: The study extrapolates the SM parameters up to the Planck scale, revealing that the measured Higgs mass aligns with the minimum allowable values of the Higgs quartic and top Yukawa couplings and the maximum permissible values of gauge couplings, considering vacuum metastability. The proximity of the Higgs mass to this critical line suggests it does not rest at the minimal energy state but rather a metastable point near a phase transition threshold.
3. Metastability and Vacuum Stability: The investigation provides an in-depth analysis of the SM vacuum state. For the current range of measurements, the vacuum state is near criticality, aligning the model in a transition state that skirts between stability and metastability. This implies that the potential for new physics could emerge from Planckian dynamics or other high-energy scales.
4. Higgs Coupling Parameters and Implications: The computation unveiled that $\lambda(\bar\mu)$ and $y_t(\bar\mu)$ (Higgs quartic and top Yukawa couplings, respectively) remain perturbative up to the Planck scale, aligning with the moderate values indicative of the potential absence of need for new physics. However, their positioning also suggests a framework for potential unification or novel scenarios tethered to the observed Higgs mass.

Theoretical and Practical Implications

• Phase Stability: Understanding the Higgs boson's near-criticality serves as a theoretical bridge to explore beyond SM physics, particularly if parameters do not naturally stabilize at low energy scales. Such insights can direct experimental searches for particles or phenomena that validate these theoretical predictions.
• Multiverse Theories and Attractors: The paper briefly speculates on a multiverse-origin for these fine-tuned settings, suggesting hypothetical dynamics at play across universes, where parameters like the Higgs mass are naturally selected to reside near critical points.

Future Developments and Speculations

• Higgs Potential at Higher Orders: Continued improvements in loop-level calculations of the Higgs potential might refine insights into whether current near-critical conditions are physical limitations or mere computational artifacts.
• Beyond Standard Model Scenarios: Should further research continue aligning these near-critical scenarios with stability boundaries, efforts could enhance significance by probing new physics frameworks — possibly those incorporating supersymmetry or other beyond SM theories.

In summary, this work consolidates a vital understanding of the Higgs boson's position relative to the potential landscape of particle physics, framing its near-criticality as both a challenge and an opportunity to decode potential underlying universality principles or hidden symmetries operating at scales currently beyond direct observational reach.