Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry

J.A. Casas; J.R. Espinosa; M. Quiros

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Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry

J.A. Casas, J.R. Espinosa, M. Quiros

High Energy Physics - Phenomenology · Submitted 30 Sep 1994 · 17 references

Pith's verdict: A real 10 GeV improvement in the SM vacuum-stability bound, driven by taking the scale dependence seriously; the stability criterion is a turnover criterion, not a tunneling calculation, and the paper says so.

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CitationJ.A. Casas, J.R. Espinosa, M. Quiros. "Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry." arXiv:hep-ph/9409458 (1994). https://pith.science/paper/DLFPXQNJ

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Editor's note

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The thing to take away: the ~10 GeV loosening of the SM Higgs lower bound is not a fudge, it comes from doing the effective potential properly. Sher and others ran the tree-level potential with RGE-improved couplings evaluated at MZ; Casas, Espinosa and Quirós use the full one-loop V with two-loop RGE and pick the scale near the field value. Figure 1 is the honest part of the paper — the solid curve is flat to about 3 GeV over a wide range of µ*, the dashed tree-level curve is not, and that gap is exactly the 10 GeV they claim. That is a clean, checkable diagnosis of where the previous number went wrong, and it is the reason to trust the shift more than the shift itself. The second real contribution is λ̃ (eq. 20): the turnover sits where the effective quartic vanishes, not the bare one, and the two differ by more than an order of magnitude (Fig. 2a). That is correct and worth knowing. The SM-versus-MSSM zoning in Fig. 6 is the part experimental colleagues will actually use, and the fits in eqs. 25–26 are a nice touch. The note added, which puts them a few GeV below Altarelli–Isidori and says so, reads like people who are not overselling. On the soft spots: the §4 criterion — no maximum below Λ, or the maximum beyond Λ — is a no-turnover criterion, not a tunneling-rate calculation. The authors state plainly that whenever there is a maximum there is a deeper minimum beyond it, so the electroweak vacuum is metastable in those cases; condition (b) only pushes the barrier past the cutoff. That is a genuine gap between what is computed and what 'stability' means, but it is the field's convention at the time, it is disclosed, and it does not invalidate the number — it just means the bound should be quoted as 'no turnover below Λ'. Minor: the error budget is quoted piecewise (3 GeV truncation, 4.25 GeV from αS, 33 GeV from Mt) rather than combined, and the MSSM side of Fig. 6 leans on their companion preprint [6], so that half of the comparison is only as good as that paper. Neither is a reason to hold it up. Who should read it: anyone quoting a Higgs mass against vacuum stability, and anyone doing SM/MSSM discrimination at the electroweak scale. It deserves referees.

Referee report

Significance

If the result holds, it materially widens the window in which a Standard Model Higgs is compatible with a stable electroweak vacuum, and it sharpens the interplay between the SM lower bound and the MSSM upper bound into a falsifiable statement about what a measured MH would rule out. The methodological strengths are real and worth naming: the use of the full one-loop V improved by two-loop RGE, the explicit demonstration of residual scale dependence in Fig. 1 with a quantified truncation error of order 3 GeV, the identification of λ̃ rather than λ as the parameter locating the turnover (Eqs. 19–20), and the provision of compact fits (Eqs. 25–26) that make the bounds directly usable by experimentalists. The paper is also candid in its note added about the concurrent Altarelli–Isidori work and the few-GeV discrepancy.

Major objections (2)

[§4, conditions (a)/(b), Eqs. (19)–(22)] The criterion adopted here is a 'no turnover below Λ' criterion, not a vacuum-lifetime criterion, and the paper says so itself in the final paragraph of §4 ('whenever there is a maximum, there is an additional minimum for a larger value of φ'). Condition (b) permits φ_MAX to sit just above Λ, in which case the barrier and the true minimum lie in a region where the SM potential is not under control and the tunneling rate is set by unknown new physics. The consequence is that the quantity bounded in Eq. (24) and plotted in Figs. 5–6 is weaker than a genuine stability bound, and the title and abstract's use of 'stability bound' overstates what is computed. A concrete test would settle the size of the effect: take the illustrative point of Fig. 3 (Mt = 160 GeV, MH = 101 GeV, Λ0 = 4×10^11 GeV) and estimate the bounce action for the φ_MAX-to-deeper-minimum transition; if the lifetime already exceeds the age of the universe for φ_MAX well below 10^19 GeV, the quoted bound could be tightened, and if not, the 'no turnover' label is the honest one. At minimum the authors should relabel the result explicitly as a no-turnover bound throughout, including the title, and state in §4 that condition (b) is necessary but not sufficient for metastability with a lifetime exceeding the age of the universe.
[§5 and Fig. 6] The headline claim of the paper (abstract:s4, that a measured Higgs mass can discard the SM, the MSSM, or both) rests entirely on the relative placement of the two curves in Fig. 6, and the MSSM upper-bound curve is imported from ref. [6], which is listed only as a preprint (CERN-TH.7334/94). The SM curve is the authors' own calculation and can be checked from the equations given; the MSSM curve cannot. Since the three-zone structure and the 'discard both' region of §5 depend on where that curve sits at the few-GeV level, the manuscript should summarize the inputs actually used (Λ_S = 1 TeV, tan β = ∞, X_t² = 6Λ_S², the treatment of the stop-mixing threshold correction to the quartic coupling, and the αS value) in enough detail that a reader can reproduce the transverse lines of Fig. 6 without consulting [6]. If a published version of [6] exists or appears, the citation should be updated.

Minor objections (8)

[§4, Eq. (22) and the sentence following it] The text states that 'depending on the sign of βλ we will have a maximum or a minimum', but Eq. (22) gives the second derivative in terms of βλ − 4γλ. The two statements differ; please state which combination actually controls the sign and give its numerical size near the turnover, since γλ is not negligible at these scales.
[§5 and Fig. 6] The SM curve is drawn for Λ = 10^19 GeV while the MSSM curve uses Λ_S = 1 TeV, so the two lines are computed at different cutoffs. The text acknowledges the consistency requirement but does not say how this choice affects the zone boundaries. Please state explicitly that using the weakest SM bound (Λ = 10^19 GeV) is conservative for the 'discard both' region of zone (iii), or correct the statement if it is not.
[§5, zone (i)] The interval 'Mt = 173 ± 4 GeV' for the crossing region is quoted without explanation of where the ±4 comes from. Please state whether it is read off Fig. 6, derived from the slopes in Eqs. (25)–(26), or taken from the CDF error, and give the criterion used to define the crossing area.
[Fig. 1 and §3] The scale-invariance plot that justifies the ~3 GeV truncation error is shown for a single parameter point (Mt = 175 GeV, Λ = 10^19 GeV, αS = 0.124). Since the paper assigns this error 'typically', please state whether the flatness was checked at other Mt and Λ, particularly at the low Mt end where the bound becomes Λ-independent, and quote the largest spread found.
[Eq. (14)] The Higgs and Goldstone contributions to the minimum condition are dropped without an estimate. Please quote the size of the neglected terms at the minimum, or state the argument that makes them negligible at the accuracy claimed.
[Fig. 2b and footnote 4] The ordinate of Fig. 2b is described only as 'a convenient choice of units' chosen 'to give a continuous and faithful representation of V in logarithmic units'. As printed the figure cannot be read quantitatively. Please give the explicit plotted variable so that the depth of the second minimum relative to the realistic one can be extracted.
[Eqs. (25)–(26)] The αS dependence is linearized over the range ±0.006. Please state the residual nonlinearity over that range, or confirm that it is below the quoted 1 GeV fit error.
[§4, final paragraph; Fig. 3 caption; Introduction] Typographical corrections: 'positive rage' should read 'positive range' in the last paragraph of §4; 'intervales' should read 'intervals' in the Fig. 3 caption; 'Rouhgly' and 'worthwile' should read 'Roughly' and 'worthwhile' in the Introduction.

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The paper

The paper claims

The Standard Model's vacuum-stability lower bound on the Higgs mass loosens by about 10 GeV once the full one-loop effective potential is used, and the paper argues the right stability criterion is the zero crossing of an effective quartic,

The reading

The Standard Model's electroweak vacuum is only conditionally stable: the top quark's Yukawa coupling drives the Higgs quartic coupling downward at high energy, so for a light enough Higgs the potential can turn over and develop a deeper minimum far from where we live. The authors recompute the resulting lower bound on the Higgs mass using the full one-loop effective potential improved by two-loop renormalization group equations, which keeps the calculation under control across a wide range of field values. They find the bound is about 10 GeV weaker than the previous estimate, and for a top mass of $174$ GeV they quote $M_H > 128$ GeV, i.e. $M_H > 95$ GeV at one sigma. The paper's sharper point is that the potential's turnover is located by an effective quartic coupling $tilde{lambda}$ (which includes the one-loop corrections), not by the bare $lambda$, and that the two can differ by more than an order of magnitude in scale. The payoff is a three-way comparison: depending on the measured top mass, a measured Higgs mass can exclude the pure Standard Model, the Minimal Supersymmetric Standard Model, or both.

What carries the argument

The load-bearing object is the effective quartic coupling $$tilde{$\lambda$} = $\lambda$ - frac{1}{$16pi^{2}$}left{$6h_t^{4}$left[logfrac{$h_t^{2}$}{2}-1right] - frac{3}{4}$g^{4}$left[logfrac{$g^{2}$}{4}-frac{1}{3}right] - frac{3}{8}($g^{2}$+g'^2)^2left[logfrac{($g^{2}$+g'^2)}{4}-frac{1}{3}right]right},$$ evaluated at the scale $mu(t) = phi_{rm ext}(t)$. Extremal points of the potential at large field satisfy $phi^2_{rm ext} = 2m^2/tilde{lambda}$, so a maximum exists only where $0 < tilde{lambda} ll 1$; the curvature there is $frac{1}{2}(beta_lambda - 4gammalambda)phi^2$, whose sign decides maximum versus minimum. This replaces the older test on the bare $lambda$ and is what makes the bound depend on the full one-loop structure of the potential rather than on the running coupling alone. The rest of the machinery is standard: two-loop renormalization group equations for all couplings, the minimum condition traded for a boundary condition on $m^2(t)$ through the measured vacuum expectation value $v = 246.22$ GeV, and the physical Higgs mass obtained from the curvature plus the renormalized self-energy.

Extended reading notes

Core claim

The paper establishes two linked results. First, the Standard Model vacuum-stability lower bound on $M_H$ is $mathcal{O}(10)$ GeV less stringent than the last previous estimate, with the difference growing from about 5 GeV at $M_t sim 130$ GeV to about 15 GeV at $M_t sim 200$ GeV; for $M_t = 174 pm 17$ GeV the quoted bound is $M_H > 128 pm 33$ GeV, i.e. $M_H > 95$ GeV at one $\sigma$. The shift comes from computing the Higgs mass with the full one-loop effective potential rather than the tree-level potential improved by running, which removes a strong and previously uncontrolled dependence on the renormalization scale. Second, the paper argues that the correct stability criterion is not $lambda(mu) > 0$ for $mu < Lambda$ but rather that the potential develop no maximum below the cutoff, or that any maximum lie beyond it; the relevant quantity is an effective quartic $tilde{lambda}$ whose zero crossing locates the maximum of $V(phi)$ and which can differ from $lambda$ by more than an order of magnitude. Setting the Standard Model cutoff at $Lambda = 10^{19}$ GeV and comparing against supersymmetric upper bounds for a decoupling scale $Lambda_S = 1$ TeV, the authors identify three regimes: for $M_t = 173 pm 4$ GeV a measured Higgs mass is compatible with the Standard Model or with supersymmetry but not both; for $M_t < 169$ GeV there is a window compatible with both; for $M_t > 177$ GeV there is a range of Higgs masses that discards both.

Load-bearing premise

The result rests on adopting the paper's own stability criterion, that the potential must have no maximum below the cutoff (or that any maximum lie beyond it), rather than the older requirement that the bare quartic coupling stay positive; if the older criterion were the physically correct one, the bound would move back toward the more stringent previous values.

Editorial extensions

If this is right

A Higgs boson found below roughly 95 GeV would be incompatible with a pure Standard Model valid up to $10^{19}$ GeV, regardless of the details of the top mass within the then-current CDF range.
For a top mass near 174 GeV, the Standard Model lower bound ($sim 128$ GeV) and the supersymmetric upper bound ($sim 126$ GeV) nearly coincide, so a single Higgs mass measurement at that value would discriminate between the two frameworks.
For top masses above about 177 GeV, there is a band of Higgs masses that is excluded by both the Standard Model stability requirement and the supersymmetric upper bound, giving a no-go window that does not depend on which framework one prefers.
The stability bound becomes insensitive to the cutoff once the top mass is small enough that $beta_lambda$ never turns negative, so for those top masses the bound is a hard statement rather than a cutoff-dependent one.
The two fit formulas, $M_H > 127.9 + 1.92(M_t - 174) - 4.25((alpha_S - 0.124)/0.006)$ for the Standard Model and $M_H < 126.1 + 0.75(M_t - 174) - 0.85((alpha_S - 0.124)/0.006)$ for supersymmetry, turn the comparison into a one-line arithmetic check once $M_t$ and $alpha_S$ are measured.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's criterion is a statement about the shape of the potential, not about the decay rate of the electroweak vacuum; a first-principles tunneling calculation through the barrier would be the natural next step, and the quoted bound should be read as the boundary of the region where such a calculation becomes relevant rather than as a lifetime measurement.
Because the shift from the older bound comes largely from how the Higgs mass is extracted rather than from new physics, similar corrections plausibly affect any other quoted stability or metastability bound computed with tree-level matching, including bounds quoted for extensions of the Standard Model.
The three-zone structure in the top-mass versus Higgs-mass plane suggests a concrete decision table: once both masses are measured with modest precision, the pair $(M_t, M_H)$ alone places the point in one of the three regions, and no further information about the ultraviolet completion is needed to draw the exclusion.
The paper's own note that $tilde{lambda}$ returns to positive values at very large scales implies the potential is bounded from below and that the failure mode is metastability rather than unboundedness; that distinction matters for how one phrases the experimental implication, since a metastable vacuum is not immediately excluded by cosmology.

Original abstract

We re-examine the lower bound on the mass of the Higgs boson, $M_H$, from Standard Model vacuum stability including next-to-leading-log radiative corrections. This amounts to work with the full one-loop effective potential, $V(\phi)$, improved by two-loop RGE, and allows to keep control of the scale invariance of $V$ in a wide range of the $\phi$-field. Our results show that the bound is ${\cal O}\ (10\ GeV)$ less stringent than in previous estimates. In addition we perform a detailed comparison between the SM lower bounds on $M_H$ and the supersymmetric upper bounds on it. It turns out that depending on the actual value of the top mass, $M_t$, the eventually measured Higgs mass can discard the pure SM, the Minimal Supersymmetric Standard Model or both.

The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,362 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.97 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We re-examine the lower bound on the mass of the Higgs boson, $M_H$, from Standard Model vacuum stability including next-to-leading-log radiative corrections. This amounts to work with the full one-loop effective potential, $V(\phi)$, improved by two-loop RGE, and allows to keep control of the scale invariance of $V$ in a wide range of the $\phi$-field. Our results show that the bound is ${\cal O}\ (10\ GeV)$ less stringent than in previous estimates. In addition we perform a detailed comparison between the SM lower bounds on $M_H$ and the supersymmetric upper bounds on it. It turns out that depending on the actual value of the top mass, $M_t$, the eventually measured Higgs mass can discard the pure SM, the Minimal Supersymmetric Standard Model or both.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We re-examine the lower bound on the mass of the Higgs boson, $M_H$, from Standard Model vacuum stability including next-to-leading-log radiative corrections.	contribution 0.98	0.89	0.05	asserted 0.61
s1	This amounts to work with the full one-loop effective potential, $V(\phi)$, improved by two-loop RGE, and allows to keep control of the scale invariance of $V$ in a wide range of the $\phi$-field.	method 0.99	0.75	0.04	asserted 0.98
s2	Our results show that the bound is ${\cal O}\ (10\ GeV)$ less stringent than in previous estimates.	result 1.00	0.95	0.57	asserted 1.00
s3	In addition we perform a detailed comparison between the SM lower bounds on $M_H$ and the supersymmetric upper bounds on it.	contribution 0.97	0.93	0.07	asserted 0.92
s4	It turns out that depending on the actual value of the top mass, $M_t$, the eventually measured Higgs mass can discard the pure SM, the Minimal Supersymmetric Standard Model or both.	interpretation 0.89	0.87	0.52	hedged possibility 0.51

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.83.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Plot of the physical Higgs mass, MH, as a function of µ(t ∗ ) in a model with Mt = 175 GeV, Λ = 1019 GeV and αS = 0.124. The solid line corresponds to our approach using the full one-loop effective potential, V , improved by two-loop RGE. The dashed line is the result using only the tree–level part of V , improved with two-loop RGE, as was done in refs. [3, 4]. Fig. 2a Plot of λ (dashed line) and λ˜ (solid line) as a function of the scale µ(t) for Λ and αS as in

**Figure 3.** Plot of λ˜ as a function of the scale µ(t) for Mt = 160 GeV, Λ = 1019 GeV and αS = 0.124. The curves are shown for intervales of 5 GeV in MH in the range 85 GeV ≤ MH ≤ 115 GeV. The thicker (tangent) line corresponds to the case MH = 101 GeV

Showing 2 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9409458 by the authors.

References

Works cited (17)

[6]

J. A. Casas, J. R. Espinosa, M. Quir´ os and A. Riotto, prep rint CERN-TH.7334/94 [hep-ph/9407389]

View on Pith Pith review arXiv
[4]

M. Sher, Phys. Lett. B317 (1993) 159; Addendum: [hep-ph/9404347]

View on Pith Pith review arXiv 1993
[1]

M. Lindner, Z. Phys. C31 (1986) 295

View on Pith 1986
[2]

M. Sher, Phys. Rep. 179 (1989) 273

View on Pith 1989
[3]

M. Lindner, M. Sher and H. W. Zaglauer, Phys. Lett. B228 (1989) 139

View on Pith 1989
[5]

C. Ford, D. R. T. Jones, P. W. Stephenson and M. B. Einhorn, Nucl. Phys. B395 (1993) 17

View on Pith 1993
[7]

M. Quir´ os, to appear in the Proceedings ofPhysics from Planck scale to electroweak scale, Warsaw, Poland, 21–24 September 1994

View on Pith 1994
[8]

B. Kastening, Phys. Lett. B283 (1992) 287; M. Bando, T. Kugo, N. Maekawa and H. Nakano, Phys. Lett. B301 (1993) 83; Prog. Theor. Phys. 90 (1993) 405

View on Pith 1992
[9]

S. Peris, Mod. Phys. Lett. 16 (1991) 1505

View on Pith 1991
[10]

H. Arason et al., Phys. Rev. D46 (1992) 3945

View on Pith 1992
[11]

N. Gray, D. J. Broadhurst, W. Grafe and K. Schilcher, Z. Phys. C48 (1990) 673

View on Pith 1990
[12]

P. Langacker, preprint UPR-0624T [hep-ph/9408310]

View on Pith Pith review arXiv
[13]

F. Abe et al., CDF Collaboration, preprint FERMILAB-PU B-94/097-E and Phys. Rev. Lett. 73 (1994) 225. 10

View on Pith 1994
[14]

Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1; J. Ellis, G. Ridolgi and F. Zwirner, Phys. Lett. B257 (1991) 83; H.E. Haber and R. Hempﬂing, Phys. Rev. Lett. 66 (1991) 1815; R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B258 (1991) 167; J.R. Espinosa and M. Quir´ os, Phys. Lett. B266 (1991) 389

View on Pith 1991
[15]

N.V. Krasnikov and S. Pokorski, Phys. Lett. B288 (1991) 184; M.A. D ´ ıaz, T.A. ter Veldius and T.J. Weiler, Vanderbilt preprint V AND–TH–9 4–14, 1994

View on Pith 1991
[16]

R. Barbieri and G.F. Giudice, Nucl. Phys. B306 (1988) 63; B. de Carlos and J.A. Casas, Phys. Lett. B309 (1993) 320

View on Pith 1988
[17]

G. Altarelli and G. Isidori, CERN–TH.7351/94. Figure Captions Fig. 1 Plot of the physical Higgs mass, MH, as a function of µ(t∗) in a model with Mt = 175 GeV, Λ = 10 19 GeV and αS = 0 .124. The solid line corresponds to our approach using the full one-loop eﬀective potential, V , improved by two-loop RGE. The dashed line is the result using only the tree–...

View on Pith Pith review arXiv

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A gauge-invariant reorganization of the Standard Model effective potential shifts the absolute stability bound to m_H > 129.40 GeV and shows the widely-quoted instability scale is not a physical quantity.
On the gauge dependence of the Standard Model vacuum instability scale
hep-ph 2014-04 conditional novelty 5.0 of 10

The field value at which the Standard Model effective potential becomes unstable is gauge dependent, shifting by about two orders of magnitude across perturbative gauge choices, while the critical Higgs mass that sepa...
Higher-order scalar interactions and SM vacuum stability
hep-ph 2014-02 conditional novelty 5.0 of 10

Adding |H|^6 and |H|^8 operators to the Standard Model potential usually shortens the electroweak vacuum lifetime, though specific coupling combinations can stabilize it.
Standard Model Vacuum Stability and Weyl Consistency Conditions
hep-ph 2013-06 conditional novelty 5.0 of 10

A truncation scheme for standard-model beta functions that respects Weyl consistency conditions shifts the calculated metastability boundary only modestly relative to the conventional three-loop-everywhere treatment.
The Higgs Mass as a Signature of Heavy SUSY
hep-ph 2013-01 conditional novelty 5.0 of 10

Imposing Higgs mass-parameter unification at the grand unification scale and running down through a high-scale supersymmetry breaking scenario yields a Higgs mass of 126 ± 3 GeV for SUSY scales above 10^10 GeV, matchi...
The top quark and Higgs boson masses and the stability of the electroweak vacuum
hep-ph 2012-07 accept novelty 5.0 of 10

Extracting the top quark mass from the Tevatron top-pair cross section rather than from kinematic reconstruction gives 173.3 +/- 2.8 GeV, which loosens the electroweak vacuum stability bound to 129.8 +/- 5.6 GeV and l...
A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations
hep-th 2012-04 conditional novelty 5.0 of 10

A 125 GeV Higgs mass is consistent with a shift-symmetric Higgs Kähler potential that sets the quartic coupling to zero at a high supersymmetry-breaking scale, and such a symmetry may arise in D-brane compactifications.
Impact of massive neutrinos on the Higgs self-coupling and electroweak vacuum stability
hep-ph 2012-03 conditional novelty 5.0 of 10

Large flavor rotations in the Dirac neutrino Yukawa matrix let TeV-scale right-handed neutrinos lower the electroweak vacuum stability cutoff and narrow the Higgs mass window, contrary to the naive expectation that lo...
Complex Scalar Singlet Dark Matter: Vacuum Stability and Phenomenology
hep-ph 2012-02 conditional novelty 5.0 of 10

The complex scalar singlet dark matter model survives all current constraints only if new physics enters below about 10^12 GeV, and is essentially excluded if the cutoff reaches the GUT scale.
Planck Scale Boundary Conditions and the Higgs Mass
hep-ph 2011-12 accept novelty 5.0 of 10

Imposing Planck-scale boundary conditions on the Higgs quartic coupling and running them down with two-loop RGEs predicts a Higgs mass of 127 plus or minus 5 GeV for lambda(M_pl)=0, and 127-142 GeV across several such...
SUSEFLAV: program for supersymmetric mass spectra with seesaw mechanism and rare lepton flavor violating decays
hep-ph 2011-09 conditional novelty 5.0 of 10

SuSeFLAV computes MSSM mass spectra with full 3x3 flavor mixing and Type-I seesaw, plus lepton-flavor-violating observables, as a downloadable Fortran package.
Vacuum Stability, Perturbativity, and Scalar Singlet Dark Matter
hep-ph 2009-10 conditional novelty 5.0 of 10

Adding a Z2 real scalar singlet to the Standard Model lowers both the vacuum-stability and perturbativity bounds on the Higgs mass, and vacuum stability can bound the singlet dark matter mass and self-coupling.
The Probable Fate of the Standard Model
hep-ph 2009-06 accept novelty 5.0 of 10

Combining two-loop Standard Model running with a global electroweak fit, the probability that the Higgs self-coupling blows up below the Planck scale is below 1%, while survival and metastability remain viable.
Standard Model Higgs boson mass from inflation: two loop analysis
hep-ph 2009-04 conditional novelty 5.0 of 10

Two-loop corrections place the Higgs mass window for successful Standard Model Higgs inflation at roughly 126 to 194 GeV, with spectral index n_s about 0.97 and tensor-to-scalar ratio r about 0.0034.
Exploring the Hyperchargeless Higgs Triplet Model up to the Planck Scale
hep-ph 2016-10 conditional novelty 4.0 of 10

A real hypercharge-zero scalar triplet added to the Standard Model can accommodate a stable or metastable electroweak vacuum, a viable dark matter candidate above about 1.8 TeV, and Starobinsky-like inflation, within ...
Higgs vacuum metastability in primordial inflation, preheating, and reheating
hep-ph 2016-02 conditional novelty 4.0 of 10

Couplings that keep the Higgs vacuum stable during inflation trigger parametric resonance and thermal destabilization afterward, so the metastability problem persists unless the inflation energy scale is far below the...
Electroweak Vacuum Stability and Diphoton Excess at 750 GeV
hep-ph 2015-12 conditional novelty 4.0 of 10

In the minimal singlet-scalar plus vector-like-fermion explanation of the 750 GeV diphoton excess, the parameter region that fits the signal has no overlap with the region that keeps the electroweak vacuum stable to h...
A study of electroweak vacuum metastability with a singlet scalar dark matter
hep-ph 2014-07 conditional novelty 4.0 of 10

A gauge-singlet scalar dark matter candidate raises the Higgs vacuum instability scale by roughly an order of magnitude and relaxes the exclusion of electroweak vacuum stability from about 3 sigma to about 1.1 sigma.
A Possible Explanation of Low Energy $\gamma$-ray Excess from Galactic Centre and Fermi Bubble by a Dark Matter Model with Two Real Scalars
hep-ph 2013-12 conditional novelty 4.0 of 10

A two-scalar dark matter model, tuned to CDMS II, CoGeNT, CRESST II or XENON 100 plus Planck relic density, reproduces the low-energy gamma-ray excess from the Galactic Centre and Fermi Bubbles and prefers flat halo p...
Vacuum Stability Constraints on the Minimal Singlet TeV Seesaw Model
hep-ph 2012-12 conditional novelty 4.0 of 10

In the minimal linear seesaw with TeV singlets, electroweak vacuum metastability caps the Dirac neutrino Yukawa at roughly 0.48, and mu to e gamma tightens it further for normal hierarchy.
LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet
hep-ph 2007-06 conditional novelty 4.0 of 10

A single real scalar singlet added to the Standard Model either dilutes LHC Higgs signals through mixing or hides the Higgs behind invisible decays, and precision electroweak data plus the relic density pin down which.
Cosmological Aspects of Higgs Vacuum Metastability
astro-ph.CO 2018-09 accept novelty 3.0 of 10

The Standard Model electroweak vacuum is metastable for central Higgs and top masses, and cosmological epochs from inflation to reheating can constrain or trigger its decay.
Is there a new physics between electroweak and Planck scales?
hep-th 2007-08 conditional novelty 3.0 of 10

The paper argues that the Standard Model plus three sub-electroweak singlet fermions and a light inflaton can explain neutrino masses, dark matter, baryon asymmetry, and inflation without any new scale between the wea...
The Higgs boson, naturalness, and the Universe
hep-ph 2026-11 conditional novelty 2.0 of 10

A review making the case that the Standard Model and the νMSM, with the Higgs as inflaton, can explain inflation, reheating, baryogenesis, and dark matter, and that naturalness is not a physical problem.

How later papers used it

69 later papers cite it

Evidence: substantial. 69 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 90 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 3 used its method or tool and 1 compared its own results with it.

Uses its method or tool 3 of 5 papers with this label

Gave its effective potential for h much greater than v, with running couplings evaluated at the scale h, following this paper.

Investigating the near-criticality of the Higgs boson (2013) · 0.88 · paraphrased: the licence does not allow quoting
Followed this paper's result for the improved Higgs potential, referring the reader there for details.

Emergent Weak Scale from Cosmological Evolution and Dimensional Transmutation (2015) · 0.82 · paraphrased: the licence does not allow quoting
Used this paper's one-loop corrected potential with running couplings, including one-loop corrections to the renormalization group equations as given in another work.

Leptogenesis via Higgs Condensate Relaxation (2015) · 0.89 · paraphrased: the licence does not allow quoting

Compares with it 1 of 2 papers with this label

Said that its potential can be seen to resemble very much the 1-loop flat space result of this paper.

Vacuum Stability in the Early Universe and the Backreaction of Classical Gravity (2017) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

63 arXiv papers cite this in 82 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 59 sentences without a confident label

Contests it 1 paper

This mismatch can be explained by the omission of two-loop QCD matching condition by the authors of Refs. [ref] , as they only considered one-loop QCD, electroweak and QED contribution in the top mass matching condition.

Planck Scale Boundary Conditions and the Higgs Mass · Boundary conditions on lambda at the Planck scale · contest 0.81

Uses its method or tool 3 papers

([ref]), where [ref] λ_eff(h) =e^4Γ(h) [ λ(μ̅=h) + λ_eff^(1)(μ̅=h) + λ_eff^(2)(μ̅=h)].All running couplings are evaluated at $μ̅=h$.

Investigating the near-criticality of the Higgs boson · Effective potential at two loops · 0.88
To obtain the vacuum stability bound we need to consider two cases in solving the coupled differential equations [ref] : * We first impose the boundary conditions at tree-level, i.e. $λ(M_pl)=0$ and apply the one-loop beta functions and anomalous dimension equations in solving the RGEs numerically. * Two-loop beta functions and anomalous dimension for $m$ are considered in our RGE and the effective potential is considered in one-loop approximation.

Planck Scale Boundary Conditions and the Higgs Mass · Boundary conditions on lambda at the Planck scale · 0.92
In our analysis, we have used the one-loop corrected potential [ref] , with running couplings (including one-loop corrections to the renormalization group (RG) equations, as given in [ref] ).

Leptogenesis via Higgs Condensate Relaxation · Effective Potential · 0.89

Uses its data or values 3 papers

The values of $n_i$, $κ_i$ and $κ_i'$ are given in the eqn.(4) in [ref] .

Constraining minimal Type-III Seesaw Model from naturalness, Lepton Flavor Violation and Electroweak Vacuum stability · Vacuum Stability · 0.80
In Eqs. [ref], and $M_i(ϕ)$ is given by [equation] The values of $n_i$ , $κ_i$ and $κ_i^'$ in the SM can be found in Eq. (4) in Ref. [ref] in the Landau gauge and in Ref. [ref] both in the Fermi gauge and in the $R_ξ$ gauge.

Fate of false vacuum in singlet-doublet fermion extension model with RG improved effective action · Effective potential and RG improved Effective potential · 0.80
The values of $n_i$, $κ_i$ and $κ_i'$ for the standard model are given in the eqn.(4) in [ref] .

The stability analysis of the extended singlet scalar model with two high scale minima · Stability Analysis · 0.95

Compares with it 1 paper

Comparing our vacuum stability band obtained with Casas et al. [ref] , a discrepancy of around $±[7]GeV$ for the Higgs mass value obtained via two-loop RGE is observed.

Planck Scale Boundary Conditions and the Higgs Mass · Boundary conditions on lambda at the Planck scale · 1.00

Cites it as background 15 papers

The possibility of the tunnelling from a physical electroweak symmetry breaking minimum (EWSB) to the deeper minimum located at superplanckian values of the Higgs field and corresponding instability of the observed vacuum have been widely discussed in the literature [ref] .

Domain walls and gravitational waves in the Standard Model · Introduction · 0.94
It is well-known that in the SM, $(h)$ can develop a minimum at large values of $h$ (i.e., $h>>v_0$) that is deeper than the electroweak minimum[For a comprehensive review, see Ref. [ref] and the references therein; also, see Refs. [ref] .].

Vacuum Stability, Perturbativity, and Scalar Singlet Dark Matter · Vacuum Stability & Perturbativity · 1.00
This includes the well-known $β$-functions that can be calculated in flat space and can be found from standard references, see for example [ref] , and the ones connected to the dynamics of a curved spacetime.

The 1-loop effective potential for the Standard Model in curved spacetime · The $β$-functions · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [6]

J. A. Casas, J. R. Espinosa, M. Quir´ os and A. Riotto, prep rint CERN-TH.7334/94 [hep-ph/9407389]

View on Pith Pith review arXiv

[2] [4]

M. Sher, Phys. Lett. B317 (1993) 159; Addendum: [hep-ph/9404347]

View on Pith Pith review arXiv 1993

[3] [1]

M. Lindner, Z. Phys. C31 (1986) 295

View on Pith 1986

[4] [2]

M. Sher, Phys. Rep. 179 (1989) 273

View on Pith 1989

[5] [3]

M. Lindner, M. Sher and H. W. Zaglauer, Phys. Lett. B228 (1989) 139

View on Pith 1989

[6] [5]

C. Ford, D. R. T. Jones, P. W. Stephenson and M. B. Einhorn, Nucl. Phys. B395 (1993) 17

View on Pith 1993

[7] [7]

M. Quir´ os, to appear in the Proceedings ofPhysics from Planck scale to electroweak scale, Warsaw, Poland, 21–24 September 1994

View on Pith 1994

[8] [8]

B. Kastening, Phys. Lett. B283 (1992) 287; M. Bando, T. Kugo, N. Maekawa and H. Nakano, Phys. Lett. B301 (1993) 83; Prog. Theor. Phys. 90 (1993) 405

View on Pith 1992

[9] [9]

S. Peris, Mod. Phys. Lett. 16 (1991) 1505

View on Pith 1991

[10] [10]

H. Arason et al., Phys. Rev. D46 (1992) 3945

View on Pith 1992

[11] [11]

N. Gray, D. J. Broadhurst, W. Grafe and K. Schilcher, Z. Phys. C48 (1990) 673

View on Pith 1990

[12] [12]

P. Langacker, preprint UPR-0624T [hep-ph/9408310]

View on Pith Pith review arXiv

[13] [13]

F. Abe et al., CDF Collaboration, preprint FERMILAB-PU B-94/097-E and Phys. Rev. Lett. 73 (1994) 225. 10

View on Pith 1994

[14] [14]

Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1; J. Ellis, G. Ridolgi and F. Zwirner, Phys. Lett. B257 (1991) 83; H.E. Haber and R. Hempﬂing, Phys. Rev. Lett. 66 (1991) 1815; R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B258 (1991) 167; J.R. Espinosa and M. Quir´ os, Phys. Lett. B266 (1991) 389

View on Pith 1991

[15] [15]

N.V. Krasnikov and S. Pokorski, Phys. Lett. B288 (1991) 184; M.A. D ´ ıaz, T.A. ter Veldius and T.J. Weiler, Vanderbilt preprint V AND–TH–9 4–14, 1994

View on Pith 1991

[16] [16]

R. Barbieri and G.F. Giudice, Nucl. Phys. B306 (1988) 63; B. de Carlos and J.A. Casas, Phys. Lett. B309 (1993) 320

View on Pith 1988

[17] [17]

G. Altarelli and G. Isidori, CERN–TH.7351/94. Figure Captions Fig. 1 Plot of the physical Higgs mass, MH, as a function of µ(t∗) in a model with Mt = 175 GeV, Λ = 10 19 GeV and αS = 0 .124. The solid line corresponds to our approach using the full one-loop eﬀective potential, V , improved by two-loop RGE. The dashed line is the result using only the tree–...

View on Pith Pith review arXiv