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Higgs Boson Mass, Proton Decay, Naturalness and Constraints of LHC and Planck Data

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ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Mengxi Liu, Pran Nath

High Energy Physics - Phenomenology · Submitted 29 Mar 2013 · 85 references

Pith's verdict: The Higgs-mass sensitivity of the p → ν̄K+ lifetime is the real result and it holds up; the naturalness claim in s6 is close to a tautology of the fine-tuning measure the authors chose.

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arXiv ID1303.7472 (version 1)
Pith ID7JLN2PEQ, Pith's permanent record of this paper and its review
CitationMengxi Liu, Pran Nath. "Higgs Boson Mass, Proton Decay, Naturalness and Constraints of LHC and Planck Data." arXiv:1303.7472 (2013). https://pith.science/paper/7JLN2PEQ
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The paper

The paper claims

In supergravity unified models the 126 GeV Higgs mass implies multi-TeV sfermions, making the p to anti-neutrino K+ lifetime extremely sensitive to the Higgs mass and shifting naturalness arguments toward a several-TeV SUSY scale.

The reading

Supersymmetric grand unified theories predict that the proton can decay, most likely into a anti-neutrino plus a K+ meson. The decay rate depends on the masses of the supersymmetric partners of quarks and leptons, because those particles run in the loop diagrams that mediate the decay. The authors point out that the newly measured Higgs boson mass of about 126 GeV requires large quantum corrections, and those corrections in turn require the sfermions to be heavy, in the several-TeV range. Heavier sfermions suppress the proton decay rate, so the proton lives longer. The paper scans the parameter space of two versions of supergravity unification, one with universal and one with non-universal gaugino masses, applying LHC, LEP, B-physics, g-2, and Planck dark matter constraints. It finds that the proton lifetime changes by up to two orders of magnitude when the Higgs mass is shifted by five to ten GeV, and that almost all surviving parameter points sit on the so-called Hyperbolic Branch of radiative electroweak symmetry breaking rather than the Ellipsoidal Branch or Focal Point region. Finally, the authors define a composite fine-tuning measure that multiplies an electroweak fine-tuning factor by a proton-stability factor, and conclude that this combined measure is minimized at scalar masses of several TeV.
Extended reading notes

Core claim

The paper's load-bearing assertion, from abstract:s2, is that over the allowed parameter space of supergravity unified models the proton lifetime for p to anti-neutrino K+ is highly sensitive to the Higgs boson mass, with a few-GeV shift changing the lifetime by as much as two orders of magnitude or more. If correct, this ties a measured quantity (the Higgs mass) to an unmeasured one (the proton lifetime) tightly enough that a future proton decay signal or null result would constrain the SUSY spectrum, and it makes the p to anti-neutrino K+ channel the priority target for next-generation detectors.

Load-bearing premise

The absolute proton lifetime, and therefore the proton-stability fine-tuning factor F_pd = 4e33 yr divided by the predicted lifetime (Eq. 24), is normalized by an effective Higgs triplet mass M_eff_H3/M_G that the authors choose by hand as 10, 25, or 50 (Sec. III, discussion around Eq. 9 and the Fig. 2 and Fig. 3 captions). The paper is explicit that it does not commit to a GUT structure and that M_eff_H3 can be made much larger than the GUT scale. Because F_pd is defined as a ratio to the experimental limit, the choice of M_eff_H3 directly sets the naturalness conclusion, so the claim that combined fine tuning favors several-TeV scalars rests on a knob rather than on a derived quantity.

Original abstract

A Higgs boson mass $\sim 126$ GeV as determined by the LHC data requires a large loop correction which in turn implies a large sfermion mass. Implication of this result for the stability of the proton in supersymmetric grand unified theories is examined including other experiments constraints along with the most recent result on cold dark matter from Planck. It is shown that over the allowed parameter space of supergravity unified models, proton lifetime is highly sensitive to the Higgs boson mass and a few GeV shift in its mass can change the proton decay lifetime for the mode $p\to \bar \nu K^+$ by as much as two orders of magnitude or more. An analysis is also given on the nature of radiative breaking of the electroweak symmetry in view of the high Higgs boson, and it is shown that most of the parameter space of universal and non-universal supergravity unified models lies on the Hyperbolic Branch of radiative breaking of the electroweak symmetry, while the Ellipsoidal Branch and the Focal Point regions are highly depleted and contain only a very small region of the allowed parameter space. Also discussed are the naturalness criteria when the proton stability constraints along with the electroweak symmetry breaking are considered together. It is shown that under the assumed naturalness criteria the overall fine tuning is improved for larger values of the scalar mass with the inclusion of the proton stability constraint. Thus the naturalness criteria including proton stability along with electroweak symmetry breaking constraints tend to favor the weak scale of SUSY in the several TeV region. Implications for the discovery of supersymmetry in view of the high Higgs mass are briefly discussed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,564 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.17 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A Higgs boson mass $\sim 126$ GeV as determined by the LHC data requires a large loop correction which in turn implies a large sfermion mass. Implication of this result for the stability of the proton in supersymmetric grand unified theories is examined including other experiments constraints along with the most recent result on cold dark matter from Planck. It is shown that over the allowed parameter space of supergravity unified models, proton lifetime is highly sensitive to the Higgs boson mass and a few GeV shift in its mass can change the proton decay lifetime for the mode $p\to \bar \nu K^+$ by as much as two orders of magnitude or more. An analysis is also given on the nature of radiative breaking of the electroweak symmetry in view of the high Higgs boson, and it is shown that most of the parameter space of universal and non-universal supergravity unified models lies on the Hyperbolic Branch of radiative breaking of the electroweak symmetry, while the Ellipsoidal Branch and the Focal Point regions are highly depleted and contain only a very small region of the allowed parameter space. Also discussed are the naturalness criteria when the proton stability constraints along with the electroweak symmetry breaking are considered together. It is shown that under the assumed naturalness criteria the overall fine tuning is improved for larger values of the scalar mass with the inclusion of the proton stability constraint. Thus the naturalness criteria including proton stability along with electroweak symmetry breaking constraints tend to favor the weak scale of SUSY in the several TeV region. Implications for the discovery of supersymmetry in view of the high Higgs mass are briefly discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A Higgs boson mass $\sim 126$ GeV as determined by the LHC data requires a large loop correction which in turn implies a large sfermion mass. background 0.41 0.18 0.10 asserted 0.98
s1 Implication of this result for the stability of the proton in supersymmetric grand unified theories is examined including other experiments constraints along with the most recent result on cold dark matter from Planck. contribution 0.95 0.65 0.05 asserted 0.51
s2 It is shown that over the allowed parameter space of supergravity unified models, proton lifetime is highly sensitive to the Higgs boson mass and a few GeV shift in its mass can change the proton decay lifetime for the mode $p\to \bar \nu K^+$ by as much as two orders of magnitude or more. result 1.00 0.85 0.23 asserted 1.00
s3 An analysis is also given on the nature of radiative breaking of the electroweak symmetry in view of the high Higgs boson, and it is shown that most of the parameter space of universal and non-universal supergravity unified models lies on the Hyperbolic Branch of radiative breaking of the electroweak symmetry, while the Ellipsoidal Branch and the Focal Point regions are highly depleted and contain only a very small region of the allowed parameter space. result 0.95 0.89 0.12 asserted 1.00
s4 Also discussed are the naturalness criteria when the proton stability constraints along with the electroweak symmetry breaking are considered together. contribution 0.99 0.60 0.05 unclear 0.72
s5 It is shown that under the assumed naturalness criteria the overall fine tuning is improved for larger values of the scalar mass with the inclusion of the proton stability constraint. result 0.96 0.88 0.15 asserted 1.00
s6 Thus the naturalness criteria including proton stability along with electroweak symmetry breaking constraints tend to favor the weak scale of SUSY in the several TeV region. interpretation 0.79 0.84 0.54 asserted 0.72
s7 Implications for the discovery of supersymmetry in view of the high Higgs mass are briefly discussed. interpretation 0.83 0.42 0.04 unclear 0.96

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from analysis of existing data 0.60.

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. FIG. 1: The parameter points in the
Figure 2. FIG. 2: An exhibition of the sensitive dependence of the proton lifetime for the decay mode
Figure 3. FIG. 3: An exhibition of the partial lifetime for the decay mode
Figure 4. FIG. 4: Top left panel: Exhibition of the Focal Curve HB/FC1 of Table II with non-universalities in the gaugino sector. Here
Figure 5. FIG. 5: Exhibition of HB (red), EB (blue), FP (green) parameter points for NuSUGRA using the inputs given in Sec.(II). All
Figure 6. FIG. 6: An exhibition of the dependence of the proton lifetime for the decay mode
Figure 7. FIG. 7: Left panel: The proton lifetime shown as blue squares over the allowed parameter space in NuSUGRA models which
Figure 8. FIG. 8: A display of the fine tuning as defined by Eqs.(22-25) vs the scalar mass
Figure 9. FIG. 9: The upper panels: RG evolution of

Figures reproduced from arXiv:1303.7472 by the authors.

References
How the literature uses it

32 arXiv papers cite this in 44 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 · 37 sentences without a confident label

Uses its method or tool 1 paper
  • In this case a more appropriate object to consider is a composite fine tuning $F$ defined by [ref] [equation] An analysis of fine tunings defined by <ref>, <ref> and <ref> is given in Fig. 8 of [ref] .

    Supersymmetry after the Higgs · Fine tuning · 0.89

Cites it as support 3 papers
Cites it as background 3 papers

What it cites · 26 sentences without a confident label

Uses data or values from 8 papers
Cites as background 17 papers
  • In supersymmetric GUTs proton decay from dimension five operators depends very sensitively on the sparticle spectrum since the sparticle spectrum enters in the dressing loop diagrams which involve the exchange of squarks and sleptons, gluinos, charginos, and neutralinos [ref] (for recent reviews see [ref] ).

    Fundamental Physics at the Intensity Frontier · Proton stability · 0.93

  • In supersymmetric GUTs proton decay from dimension five operators depends very sensitively on the sparticle spectrum since the sparticle spectrum enters in the dressing loop diagrams which involve the exchange of squarks and sleptons, gluinos, charginos, and neutralinos [ref] (for recent reviews see [ref] ).

    DUSEL Theory White Paper · Proton stability · 0.93

  • We will also consider NuSUGRA models (for recent works on NuSUGRA see [ref] and for a review see [ref] .

    Gluino NLSP, Dark Matter via Gluino Coannihilation, and LHC Signatures · Higgs mass and branches of radiative breaking of the electroweak symmetry · 0.92

Discussion

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