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Cited by 106Particle physics theoretical and experimental studiesBlack Holes and Theoretical PhysicsCosmology and Gravitation Theories

The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index; 7 of the 31 sources its claims cite were checked for support.

The fate of the Higgs vacuum

Open access
Burda, Philipp, Gregory, Ruth, Moss, Ian G.·2016·Journal of High Energy Physics
DOI 10.1007/jhep06(2016)025
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Abstract

We have recently suggested that tiny black holes can act as nucleation seeds for the decay of the metastable Higgs vacuum. Previous results applied only to the nucleation of thin-wall bubbles, and covered a very small region of parameter space. This paper considers bubbles of arbitrary profile and reaches the same conclusion: black holes seed rapid vacuum decay. Seeded and unseeded nucleation rates are compared, and the gravitational back reaction of the bubbles is taken into account. The evolution of the bubble interior is described for the unseeded nucleation. Results are presented for the renormalisation group improved Standard Model Higgs potential, and a simple effective model representing new physics.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper shows that tiny black holes can seed rapid decay of the metastable Higgs vacuum for arbitrary bubble-wall profiles, not just thin-wall bubbles. It finds that a single primordial black hole in the observable universe would cause Standard Model Higgs vacuum decay, while beyond-Standard-Model or quantum-gravity corrections can suppress the rate only under restrictive conditions.

Key findings

  • Black-hole-seeded vacuum decay is robust across Higgs-potential parameters: the bounce action can be far smaller than the O(4) unseeded action, so “vacuum decay is enhanced by black holes in this mass range.”
  • The branching ratio of tunnelling to Hawking evaporation is \(\Gamma_D/\Gamma_H \approx 43.8\,(M_+^2/M_p^2)\,B^{1/2}e^{-B}\). Vacuum decay dominates when the black-hole mass is \(10^5\)–\(10^9\) times the reduced Planck mass, depending on top quark mass in the range 172–174 GeV; corresponding Hawking temperatures are \(10^{13}\)–\(10^9\) GeV and decay half-lives \(10^{-24}\)–\(10^{-12}\) s.
  • A single primordial black hole in the observable universe would cause decay of the Standard Model Higgs vacuum and therefore contradict the Standard Model. A stable Higgs vacuum requires new physics to change the barrier at energies around \(10^{10}\)–\(10^{14}\) GeV; quantum-gravity \(\phi^6\) terms can suppress decay unless the high-energy vacuum becomes the false vacuum, which happens when \(\lambda_6\) is around \(10^{12}\).
  • For non-negative \(\lambda_6\), unseeded vacuum decay rates are extremely small. Negative \(\lambda_6\) can enhance decay, but the Higgs field at the bubble centre lies very close to the Planck scale and the effective-potential reliability becomes questionable.

Methods

  • The authors numerically solve the coupled Euclidean Einstein-Higgs equations for O(4)-symmetric instantons without assuming the thin-wall approximation, using a three-parameter fit to the renormalisation-group improved Higgs potential, \(\lambda_{\rm eff}(\phi)=\lambda_*+b\ln(\phi/M_p)^2+c\ln(\phi/M_p)^4\), plus possible \(\phi^6/M_p^2\) terms.
  • For black-hole-seeded decay, they construct static SO(3)-symmetric Euclidean instantons with a Schwarzschild-like mass term, integrate from the horizon using a shooting method, and compute the tunnelling exponent from horizon areas or mass parameters, \(B=(M_+^2-\mu_-^2)/(2M_p^2)\).
  • They compare seeded and unseeded nucleation rates, include gravitational back reaction, and analytically continue the O(4) bounce to Lorentzian spacetime to follow the bubble interior evolution toward a crunch singularity.

Limitations

  • Paper-stated: the instanton approach and its interpretation are well understood in flat spacetime but not rigorously described in curved space; questions remain about Hawking radiation in tunnelling, global spacetime structure, and why the tunnelling rate is independent of the conical-singularity angle.
  • Paper-stated: for negative \(\lambda_6\), the Higgs field at the bubble centre lies near the Planck scale, so the effective field theory justification fails and enhancement cannot be confirmed for the potential and top-quark mass ranges considered.
  • Paper-stated: quantum corrections to the potential may be affected by spacetime curvature, though this can be partly sidestepped using black-hole monopoles. Evident from the text: the numerical solutions rely on shooting and finite-radius boundary conditions, with care needed to ensure robustness to changes in \(\rho_{\max}\) and \(\phi(\rho_{\max})\).

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/jhep06(2016)025

Cites

55 of 55 references verified0 citation errors · 0 not checkable

Statistics

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Verification

Claims the paper makes

7 of 31 cited sources checked · 3 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    In [29], preliminary evidence was provided that the parameter space restriction was an artefact of the constraints imposed on the potential by demanding a thin-wall approximation.

    “In [29], we provided preliminary evidence that this parameter space restriction was an artefact of the constraints imposed on the potential by demanding that it allow a thin-wall approximation for the instanton.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source
  • Premisecitation

    In [29,30], the tunnelling exponent did not depend on the periodicity of the Euclidean time (temperature).

    “In [29,30], we found that the tunnelling exponent did not depend on the periodicity of the Euclidean time, in other words, on the value of the temperature.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source

      Our copy says that for static instantons the action is given by the black-hole horizon-area terms in Eq. (5), and that the calculation treats conical deficits when periodicities differ. This supports independence from Euclidean-time periodicity for the static solutions studied, but the paper also gives a more general instanton action with an additional integral; it does not establish the claim for tunnelling exponents without that qualification. The supplied passages have no page labels. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source
  • Findingown data

    Black holes seed rapid vacuum decay.

    “This paper considers bubbles of arbitrary profile and reaches the same conclusion: black holes seed rapid vacuum decay.”
    Quote in the paperSubstantial claim
  • Findingnone given

    For λ_6 = 0, the leading order behaviour of the solutions near ρ_s can be determined analytically, with a ∝ (ρ_s - ρ).

    “For λ 6 = 0, the leading order behaviour of the solutions when ρ ≈ ρ s can be determined analytically, a ∝ (ρ s -ρ)”
    Quote in the paperNot a substantial claim
  • Findingreasoning

    The probability of vacuum decay in the lifetime of the universe is P_D ∼ exp(540 + 2 ln B - B), which is comfortably small for the range of B values shown in figure 3.

    “We take the size of the universe to be around 10 61 M -1 p , leading to P D ∼ exp(540 + 2 ln B -B), which is comfortably small for the range of B values shown in figure 3.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one. 28
  • The quote only partly states this claim. 1
  • Probably not a substantial claim. 12

  • It may state two separate claims as one.

    Premisecitation

    For each seed mass black hole, there exists a unique least action instanton with a unique remnant black hole mass.

    “These Euclidean solutions exist in principle with all possible values of interior and exterior mass terms, however, for each seed (exterior) mass black hole, there exists a unique least action instanton with a unique remnant (interior) black hole mass.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source

      The passage on the critical seed mass (section labeled Abstract; page unavailable) describes a static bubble solution and says that bubbles formed at higher seed masses leave an interior black-hole remnant. It does not establish a unique least-action instanton or a unique remnant mass for each seed mass; at lower seed masses, it says the bubble initially removes the black hole. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source

  • It may state two separate claims as one.

    Premisecitation

    For very small seed masses, there are instanton solutions that remove the black hole, and the solution has the form of a perturbed CDL instanton.

    “For very small seed masses, there are instanton solutions that remove the black hole, and the solution has the form of a perturbed CDL instanton.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source

      The passage labeled “Abstract” says that when the seed black-hole mass is first switched on, the bubble nucleates by removing the black hole. It also describes extending the Coleman–de Luccia thin-wall method to include a black hole, but does not establish that the resulting solution has the form of a perturbed CDL instanton. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source

      Section 3.2 states that for seed masses below the critical mass, the dominant tunnelling process removes the black hole. Sections 3 and 3.1 use the black-hole-free CDL solution as a comparator, but the passages do not establish that the small-seed-mass instanton has the form of a perturbed CDL instanton. Page numbers are unavailable in our copy. (LLM, conf=0.83)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Findingown data

    Negative values of λ_6 raise the value of φ at the centre of the bubble above the Planck scale, so the effective field theory justification fails and enhancement of tunnelling cannot be confirmed for the considered potential and top quark mass ranges.

    “Negative values of λ 6 raise the value of φ at the centre of the bubble to be above the Planck scale M p .The justification for using the effective field theory fails, and we cannot confirm enhancement of the tunnelling rate with the potential and top quark mass ranges we are considering here.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data

    The three-parameter model for λ_eff gives a much better fit over the range of large φ relevant for tunnelling than two-parameter fits.

    “Although two-parameter fits have been used before [5,29,30], we use here a three parameter model,”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingnone given

    The centre of the bounce solution has negative vacuum energy, and the spacetime geometry around ρ = 0 has negative curvature.

    “The centre of the bounce solution has negative vacuum energy, and the spacetime geometry around ρ = 0 has negative curvature.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingnone given

    The bounce solution in figure 2 has r_b ∼ 100 M_p^{-1}.

    “For example, the bounce solution in figure 2 has r b ∼ 100M -1 p .”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    The action of the bounce solution depends most importantly on λ_* (which varies with top quark mass) and very little on b.

    “The most important dependence is on the parameter λ * , which varies with the value of the top quark mass.There is very little dependence on the b parameter.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The main uncertainty in the Higgs potential is due to the uncertainty of the top quark mass.

  • It may state two separate claims as one.

    Findingreasoning

    As expected, positive values of λ_6 increase the bounce action and reduce the vacuum decay rate.

    “As expected, positive values of λ 6 increase the action and reduce the vacuum decay rate.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    The φ-field rolls logarithmically to large values and the AdS spacetime develops a crunch singularity in the interior solution shown.

    “Unsurprisingly, since the potential in this example reaches large negative values, the φ-field rolls logarithmically to large values and the 'AdS' spacetime develops a crunch singularity.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The O(4) bounce action B has principal dependence on λ*, with very weak dependence on b.

    “The principal dependence is then on the parameter λ * , which determines the large field limit of the coupling.There is a very weak dependence on the parameter b as shown.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • It may state two separate claims as one.

    Findingnone given

    The authors found a way to examine the evolution of the bubbles in real time and followed the interior towards a singularity.

    “Nevertheless, we have found a way to examine the evolution of the bubbles in real time and followed the interior towards a singularity.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Findingnone given

    Vacuum decay can also be enhanced if the λ6 coefficient in the potential is negative.

    “Vacuum decay can also be enhanced if the λ 6 coefficient in the potential is negative.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • It may state two separate claims as one.

    Findingnone given

    The black holes have Hawking temperatures in the range 10^13-10^9 GeV and decay half-lives ranging from 10^-24 to 10^-12 s.

    “but with Hawking temperatures in the range 10 13 -10 9 GeV their decay half-life is tiny, ranging from 10 -24 -10 -12 s.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    The μ-profile tracks the exact Schwarzschild-AdS form until the scalar starts to fall, then makes a rapid transition up to the asymptotic Schwarzschild form.

    “The µ-profile tracks the exact Schwarzschild-AdS form until the scalar starts to fall, when it makes a rapid transition up to the asymptotic Schwarzschild form.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • It may state two separate claims as one.

    Findingnone given

    As λ6 increases, the potential of the true vacuum rises and the bounce solution starts to resemble a region of true vacuum surrounded by a thin-wall transition to the false vacuum.

    “As the value of λ 6 is increased, the potential of the true vacuum rises and the bounce solution starts to resemble a region of true vacuum surrounded by a thin-wall transition to the false vacuum.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingnone given

    The bounce solution has the same profile in all four dimensions (three space and one imaginary time).

    “the bounce solution has the same profile in all four dimensions (three space and one imaginary time).”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • It may state two separate claims as one.

    Premisenone given

    In the thin-wall case, the bubble interior is in the true vacuum, but this is not true for the thick-wall case.

    “In the thin-wall case, the bubble interior is in the true vacuum, but this is not true for the thick-wall case.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Black hole instantons represent vacuum decay processes nucleated by black hole seeds, leaving behind black hole remnants when the seed mass exceeds the critical mass M_C.

    “Following this interpretation, black hole instantons represent vacuum decay processes nucleated by black hole seeds, leaving behind black hole remnants when the seed mass exceeds the critical mass M C .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. It may state two separate claims as one.

    Premisecitation

    In [27], the effect of conical deficits was carefully computed, and a potentially large enhancement of CDL rates was demonstrated for tunnelling from a positive to zero cosmological constant.

    “In [27], the effect of said conical deficits was carefully computed, and a potentially large enhancement of the CDL rates was demonstrated in the context of tunnelling from a positive to zero cosmological constant.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] R. Gregory, I.G. Moss and B. Withers, Black holes as bubble nucleation sites, JHEP 03 (2014) 081 [ arXiv:1401.0017 ] [ INSPIRE ]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisereasoning

    The action computed is gauge invariant, so fixing the time coordinate gauge at the horizon is irrelevant.

    “This means the t-coordinate is no longer the time for an asymptotic observer, however, the action we compute is gauge invariant, hence this is irrelevant.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    The interpretation of the tunnelling instanton used by Brown and Weinberg is not the same as the original CDL interpretation, and their conclusion that static instantons imply thermal tunnelling does not apply in the CDL interpretation.

    “However, the interpretation of the tunnelling instanton used by Brown and Weinberg is not the same as the original interpretation due to CDL that we use here.In particular, their conclusion that static instantons imply thermal tunnelling does not apply in the CDL interpretation.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [42] A.R. Brown and E.J. Weinberg, Thermal derivation of the Coleman-De Luccia tunneling prescription, Phys. Rev. D 76 (2007) 064003 [ arXiv:0706.1573 ] [ INSPIRE ]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    In ref. [30], the condition of metric regularity could be loosened to allow conical singularities without affecting the resulting tunnelling rate.

    “(In ref. [30] we demonstrated that the condition of metric regularity could be loosened to allow conical singularities, but the resulting tunnelling rate was unaffected.)”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source

  • It may state two separate claims as one.

    Premisereasoning

    The boundary value problem appears overdetermined, but this is because the remnant mass parameter μ_- is determined by the seed mass M_+.

    “The boundary value problem appears to be overdetermined, but this is simply because the remnant mass parameter µ - is determined by the value of the seed mass M + .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    As the wall thickens, the sharp jump in μ(r) at r_+ will be rounded off and spread out, with the function following the same broad shape but smoothly.

    “Since µ(r) responds to the energy-momentum tensor, we would expect that as the wall thickens, the sharp jump in µ(r) at r + will be rounded off and spread out, with the function following the same broad shape, but smoothly.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may state two separate claims as one.

    Premisenone given

    The single instanton picture of Coleman et al. is extremely idealised and contains no description of inhomogeneities.

    “The single instanton picture of Coleman et al. is however extremely idealised.There are no features to the solution other than the bubble -in particular, no description of inhomogeneities.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Even if the static instantons do not have the lowest action, they give an upper bound on the seeded nucleation rate, so the main point about enhancement is made a fortiori.

    “Even if these solutions do not have the lowest action, this would only mean the static instantons constructed would give an upper bound on the seeded nucleation rate, and our main point about enhancement of the decay rate is made a fortiori.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisenone given

    In black hole seeded decay, the seed black hole is not thermal but radiating into the surrounding vacuum, with different temperature spectra for outgoing and ingoing modes.

    “In black hole seeded decay, the seed black hole is not thermal, but instead radiating into the surrounding vacuum, with different temperature spectra for the outgoing and ingoing modes.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    The CDL instanton is also a good approximation to a wall of finite thickness, as the Israel equations are a leading order approximation for a thin but finite thickness wall.

    “Although Coleman and de Luccia concentrated on the gravitational instanton representing a bubble with an infinitesimally thin domain wall, the CDL instanton is also a good approximation to a wall of finite thickness, as the Israel equations are simply a leading order approximation for a thin, but finite thickness, wall [40,41].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [40] D. Garfinkle and R. Gregory, Corrections to the Thin Wall Approximation in General Relativity, Phys. Rev. D 41 (1990) 1889 [ INSPIRE ]. source
    • cites [41] F. Bonjour, C. Charmousis and R. Gregory, Thick domain wall universes, Class. Quant. Grav. 16 (1999) 2427 [ gr-qc/9902081 ] [ INSPIRE ]. source

  • It may state two separate claims as one.

    Premisecitation

    For larger black hole seeds beyond a critical mass M_C, the remnant mass is non-zero and the minimum action solution becomes static in the complex time coordinate.

    “For larger black hole seeds (beyond a critical mass M C depending on the vacuum energy and the surface tension of the wall) the remnant mass is non-zero and the minimum action solution becomes static in the complex time coordinate.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The possibility of vacuum decay caused by black holes formed from collisions was considered in refs. [29,30].

    “The possibility of vacuum decay caused by black holes formed from collisions was considered JHEP06(2016)025 in [29,30].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [29] P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [ arXiv:1501.04937 ] [ INSPIRE ]. source
    • cites [30] P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [ arXiv:1503.07331 ] [ INSPIRE ]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The instanton approach and its interpretation are based on results well understood in flat spacetimes but not rigorously described so far in the curved-space context.

    “The instanton approach, and its interpretation, are based on results which well understood in flat spacetimes but not rigorously described so far in the curved space context (although see [42,44]).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [42] A.R. Brown and E.J. Weinberg, Thermal derivation of the Coleman-De Luccia tunneling prescription, Phys. Rev. D 76 (2007) 064003 [ arXiv:0706.1573 ] [ INSPIRE ]. source
    • cites [44] V.A. Rubakov and S.M. Sibiryakov, False vacuum decay in de Sitter space-time, Theor. Math. Phys. 120 (1999) 1194 [ gr-qc/9905093 ] [ INSPIRE ]. source

  • It may state two separate claims as one.

    Interpretationreasoning

    A single primordial black hole in the observable universe would cause the decay of the Standard Model Higgs vacuum, and therefore would contradict the Standard Model.

    “The importance of these results lies in the fact that a single primordial black hole in the observable universe would cause the decay of the Standard Model Higgs vacuum, and therefore would contradict the Standard Model.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: A primordial black hole starting out with a mass around 10^12 kg would decay by Hawking evaporation to the mass scales shown in figure 8 by the present day.

  • It may state two separate claims as one.

    Interpretationreasoning

    Using dimensional analysis, the determinant factor is roughly (GM+)^-1, yielding Γ_D ≈ (B/2π)^{1/2} (GM+)^-1 e^{-B}.

    “We use dimensional analysis to obtain a rough estimate (GM + ) -1 for the determinant factor, yielding”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Study design and conductcitation

    The numerical results are cross-checked by comparing the bounce action to the thin-wall results obtained analytically in ref. [27].

    “This allows a cross-check of the numerical results by comparing the bounce action to the thin-wall results obtained analytically in ref. [27].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] R. Gregory, I.G. Moss and B. Withers, Black holes as bubble nucleation sites, JHEP 03 (2014) 081 [ arXiv:1401.0017 ] [ INSPIRE ]. source

  • It may state two separate claims as one.

    Interpretationreasoning

    The new results apply for any bubble wall profile and show that black holes are very effective seeds for vacuum decay.

    “these new results apply for any bubble wall profile and show that black holes are very effective seeds for vacuum decay.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

  • It may state two separate claims as one.

    Interpretationreasoning

    At some point, the vacuum decay rate becomes larger than the Hawking evaporation rate and the black hole seeds vacuum decay.

    “At some point, the vacuum decay rate becomes larger than the Hawking evaporation rate and the black hole seeds vacuum decay.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: A primordial black hole starting out with a mass around 10^12 kg would decay by Hawking evaporation to the mass scales shown in figure 8 by the present day.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    Static bubbles in AdS-AdS transitions would have the holographic interpretation of flows between field theories at different temperatures and different central charges.

    “Static bubbles would now have the holographic interpretation of flows between field theories at different temperatures and different central charges.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Quantum gravity effects can suppress the vacuum decay rate by contributing φ6 terms to the Higgs potential, but the vacuum decay rate still remains large unless the high-energy vacuum becomes the false vacuum, which happens when λ6 is around 10^12.

    “Looking beyond the Standard Model, quantum gravity effects can suppress the vacuum decay rate by contributing φ 6 terms to the Higgs potential, but the vacuum decay rate still remains large unless the high-energy vacuum becomes the false vacuum, which happens when the coefficient λ 6 is around 10 12 .”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.
38 of 38

  • The paper relies on this without support.

    The semi-classical approximation can be trusted for seed masses larger than the Planck mass.

    “for seed masses larger than the Planck mass, 10 -5 g, where the semi-classical approximation can be trusted”

  • The paper relies on this without support.

    The seed black hole is not thermal but radiating into the surrounding vacuum, with different temperature spectra for outgoing and ingoing modes.

    “In black hole seeded decay, the seed black hole is not thermal, but instead radiating into the surrounding vacuum, with different temperature spectra for the outgoing and ingoing modes.”

  • The paper relies on this without support.

    The main uncertainty in the Higgs potential is due to the uncertainty of the top quark mass.

    “The main uncertainty in the potential is due to the uncertainty of the top quark mass.”

  • The paper relies on this without support.

    The value of λ_eff at energies around the Higgs mass is accessible to experimental particle physics and can be fixed with some confidence.

    “Since the value of λ eff at energies around the Higgs mass is accessible to experimental particle physics, we can fix λ eff at the lower end of the range with some confidence.”

  • The authors state this as an assumption.

    The high-energy Higgs effective coupling can be described by the simplified model with parameters λ*, b, c, and λ6 used for the vacuum decay results.

    “The simplified model of the high-energy effective coupling used for vacuum decay results.”

  • The paper relies on this without support.

    A primordial black hole starting out with a mass around 10^12 kg would decay by Hawking evaporation to the mass scales shown in figure 8 by the present day.

    “A primordial black hole starting out with a mass around 10 12 kg would decay by Hawking evaporation to the mass scales shown in figure 8 by the present day.”
6 of 6

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Higher-action instantons cannot set an upper bound on the decay rate

    Minor

    If the constructed instantons do not have the lowest action, their exponentially suppressed rate is a lower bound on the rate from the lowest-action instanton, not an upper bound.

1 of 1

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Cites

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Research works printed but not linked: 1

  1. E. Greenwood, E. Halstead, R. Poltis and D. Stojkovic, Dark energy, the electroweak vacua and collider phenomenology, Phys. Rev. D 79 (2009) 103003 [ arXiv:0810.5343 ] [ INSPIRE ]. · arXiv

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Metadata

Authors
Burda, P., Gregory, R., & Moss, I. G.
Affiliations
  • Durham University (GB)
  • Perimeter Institute (CA)
  • Newcastle University (GB)
Corresponding author
Gregory, Ruth
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2016-06
Volume
2016
Issue
6
ISSN
1029-8479 (ISSN-L)
DOI
10.1007/jhep06(2016)025
OpenAlex
W2232606006
Cited by
106
References
47
Citations by year
2026: 6 · 2025: 12 · 2024: 7 · 2023: 10 · 2022: 9 · 2021: 12 · 2020: 15 · 2019: 9 · 2018: 14 · 2017: 9 · 2016: 3
FWCI
5.06
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Journal of High Energy Physics (publishedVersion, cc-by)
  • Durham Research Online (Durham University) (acceptedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Durham Research Online (Durham University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1066293)
  • Aspen Center for Physics (1066293, PHYS-1066293)
  • Government of Canada
  • Wolfson Foundation
  • Industry Canada
  • Israel Science Foundation (812/11)
  • Einstein Stiftung Berlin
  • Institut Périmètre de physique théorique
  • Engineering and Physical Sciences Research Council
  • Science and Technology Facilities Council (PHYS-1066293, ST/L000407/1, ST/J000426/1)
  • Israeli Centers for Research Excellence
  • Planning and Budgeting Committee of the Council for Higher Education of Israel
  • High Energy Physics
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
metastable vacuum, black holes, nucleation, bubble nucleation rate, gravitational backreaction, Higgs potential, beyond the Standard Model

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-11-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-11-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Cited sources are checked with a language model’s help (gpt-6-sol).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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