[Paper Review] The Fate of the Higgs Vacuum

Ruth Gregory, Ian G. Moss|arXiv (Cornell University)|Nov 15, 2016

International Science and Diplomacy4 citations

TL;DR

This paper demonstrates that tiny black holes can dramatically enhance the decay rate of the metastable Higgs vacuum by acting as nucleation sites, reducing the Euclidean action of the tunneling instanton. Numerical results show that for black holes near the Planck mass, vacuum decay via black hole catalysis dominates over Hawking evaporation, implying that either such black holes do not exist in our universe or new physics must stabilize the Higgs potential.

ABSTRACT

This talk reviews our recent work showing how tiny black holes can act as nucleation sites for the decay of the metastable Higgs vacuum. We start by discussing the formation of thin wall bubbles of true vacuum inside a false vacuum, and show how adding a black hole lowers the action of the Euclidean tunneling solution, thus strongly enhancing the probability of vacuum decay. We then review numerical results for the Higgs vacuum showing that the decay rate is even higher for these "thick wall" bubbles. The results imply either tiny black holes are not a component of our universe, or BSM corrections to the Higgs potential must stabilise our vacuum.

Motivation & Objective

• To investigate how gravitational inhomogeneities, particularly tiny black holes, affect the metastability of the Higgs vacuum in the Standard Model.
• To assess whether the presence of black holes could drastically shorten the lifetime of the false vacuum, challenging the assumption of vacuum stability.
• To determine whether the standard Coleman-de Luccia tunneling framework remains valid in the presence of black hole impurities.
• To explore the implications of these findings for cosmology and the existence of primordial black holes or new physics beyond the Standard Model.

Proposed method

• Adapted the Coleman-de Luccia formalism to include a black hole as a gravitational impurity in the Euclidean path integral approach to vacuum decay.
• Used a spherically symmetric ansatz for the metric and numerically solved the Einstein-scalar equations to find static bounce solutions on a black hole background.
• Calculated the instanton action as the difference in black hole horizon areas, B = (A₊ - A₋)/(4G), linking it to entropy change.
• Treated conical singularities in the Euclidean solution to ensure regularity and physical consistency of the tunneling configuration.
• Fitted the running Higgs self-coupling using a three-parameter analytic form λ_eff(ϕ) = λ_* + b(ln ϕ/Mp)² + c(ln ϕ/Mp)⁴ to model the potential across energy scales.
• Evaluated the vacuum decay rate using the entropy-fluctuation formula, with Γ ∝ exp(ΔS), where ΔS is the entropy difference between the initial and final states.

Experimental results

Research questions

• RQ1 Can a single tiny black hole significantly enhance the rate of false vacuum decay in the Higgs sector?
• RQ2 How does the presence of a black hole modify the Euclidean action of the tunneling instanton compared to the standard thin-wall or thick-wall scenarios?
• RQ3 What is the relative dominance of vacuum decay versus Hawking evaporation for primordial black holes near the Planck mass?
• RQ4 To what extent does the transition from thick-wall to thin-wall behavior depend on the inclusion of quantum gravity-inspired terms like λ₆ϕ⁶/Mp²?
• RQ5 What constraints do the observed stability of the universe place on the existence of primordial black holes or the structure of the Higgs potential beyond the Standard Model?

Key findings

• For black holes with mass ~10⁵ Mₚ, the vacuum decay half-life is ~10⁻²⁸ s, which is shorter than their Hawking evaporation timescale.
• The instanton action for black hole-catalyzed decay depends only on the difference in black hole horizon areas, B = (A₊ - A₋)/(4G), linking decay to entropy change.
• Numerical solutions confirm that vacuum decay becomes the dominant decay channel for black holes in the mass range where semiclassical gravity is valid.
• The transition from thick-wall to thin-wall behavior is smoothly captured by tuning the quantum gravity parameter λ₆, with larger λ₆ favoring thin-wall dynamics.
• The results imply that either primordial black holes do not exist in our universe, or new physics must stabilize the Higgs potential to prevent catastrophic vacuum decay.
• The branching ratio for vacuum decay over evaporation is strongly enhanced for black holes near the Planck mass, making decay the dominant process in the final stages of black hole evolution.