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REVIEW 3 major objections 5 minor 67 references

The Heavy Gluino in Natural No-Scale $\cal{F}$-$SU$(5)

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that No-Scale F-SU(5), with all masses set by a single parameter, remains natural and consistent with LHC data if the gluino can be as heavy as 7.5 TeV, provided a master coupling dilutes overproduced dark matter.

desk verdict A credible but incomplete case that no-scale F-SU(5) can host a ~7.5 TeV gluino if the λ6 dilution mechanism delivers what the paper delegates to an in-preparation companion. read the letter →

arxiv 1908.06149 v1 pith:ST5QPJZJ submitted 2019-08-16 hep-ph hep-ex

Thomas Ford , Tianjun Li , James A. Maxin , Dimitri V. Nanopoulos This is my paper · ORCID
classification hep-phhep-ex PACS 11.10.Kk11.25.Mj11.25.-w12.60.Jv
keywords no-scalesupergravityFlippedSU(5)gluinomasssupersymmetryrelicdensitydilutionlambda6mastercouplingLHClimitsnaturalSUSY
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the no-scale, one-parameter supersymmetric GUT model F-SU(5) can still accommodate LHC experiments even though the gluino mass lower limit now stands at 2.25 TeV. The authors show that if one drops the requirement that the neutralino be the observed dark matter and instead relies on a cosmological dilution mechanism, the model's allowed gluino mass rises to about 7.5 TeV, with the lightest supersymmetric particle at about 1.6 TeV, while keeping the Higgs mass within the measured 125 GeV window and the top quark mass within its world average. A single coupling, lambda6, governs the flaton decay that releases entropy and dilutes the relic density from values as large as 25.8 down to the observed $\Omega$ $h^{2}$ ~ 0.12. The model remains natural in the sense of no electroweak fine-tuning, with all masses scaling from one gaugino mass parameter M1/2.

What carries the argument

The machinery is the one-parameter No-Scale Supergravity boundary condition (M0 = A0 = B_mu = 0 at the string scale ~ 2e17 GeV, with everything scaling with the unified gaugino mass M1/2), plus the two vector-like flippon multiplets that flatten the SU(3) $\beta$-function and produce a spectrum ordering with the stop lighter than the gluino. The cosmological piece is the master coupling lambda6, a Yukawa coupling in the superpotential term lambda6 F H-bar phi that mixes the inflaton with a right-handed sneutrino; its flaton decay releases entropy and dilutes the LSP relic density. The combined effect of these: raising M1/2 raises the stop and gluino masses, the Higgs mass forces a lower top mass, and the lambda6 coupling rescales the dark matter abundance down to the observed value.

What would settle it

Pick the benchmark point with M1/2 = 5350 GeV (gluino 7103 GeV, relic density 25.82) and compute the flaton decay parameters (flaton mass ~$10^{4}$ GeV, VEV ~ $10^{16}$ GeV, lambda6 value) that would yield an entropy dilution factor of about 215. If the flaton decays before the LSP freezes out, or if the produced entropy is less than ~200, the relic density stays above the observed dark matter abundance and the point is excluded. More simply, when the 'in preparation' paper [53] appears with the actual dilution calculation, check whether its maximum $\Delta$ at the relevant parameters reaches the needed values.

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Extended reading notes

Core claim

The central claim is that No-Scale F-SU(5), with B_mu = 0 and no electroweak fine-tuning, is compatible with the current LHC gluino exclusion if the relic-density constraint is relaxed. The proportional scaling of all SUSY masses with M1/2 lets the gluino mass climb as M1/2 is raised; the limiting factor becomes the light Higgs mass, which grows with the stop mass and must be held near 125 GeV by lowering the top quark mass within its world-average band. The authors identify the upper limit M(gluino) ~ 7.5 TeV and M(LSP) ~ 1.6 TeV at the point where the needed top mass would fall outside the world average. Above 2.3 TeV the thermal neutralino abundance exceeds the observed dark matter density, and the paper invokes the lambda6 master coupling: the flaton decays with an entropy release $\Delta$ up to O($10^{4}$), diluting the relic density down to ~0.12. With this mechanism, the model's parameter space opens up to a heavy gluino region beyond the reach of LHC Run 2, and potentially accessible to a 100 TeV collider.

Load-bearing premise

The whole heavy-gluino region above 2.3 TeV is cosmologically viable only if the lambda6 flaton-decay mechanism can release enough entropy to dilute the neutralino relic density by up to a factor of about 200, down to the observed value, and this mechanism is imported from references rather than computed for the benchmark points here.

Editorial extensions

If this is right

  • If the claim holds, No-Scale F-SU(5) remains compatible with all current LHC and cosmology data without electroweak fine-tuning.
  • The model predicts that no gluino signal will be seen at LHC Run 2; discovery would require a 100 TeV collider for gluinos near the upper boundary.
  • The viable heavy-gluino region requires tan beta ~ 10, offering a sharp prediction for future precision measurements.
  • The relic-density dilution mechanism ties the observed dark matter abundance to the neutrino-mass and baryogenesis parameters through lambda6, making cosmology and particle physics mutually constraining within the model.

Reading between the lines

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

  • If the flaton dilution mechanism fails or its parameters cannot reach Delta ~ 200, every gluino mass above ~2.3 TeV in this model would overproduce dark matter, so the paper's central phenomenological claim would collapse; the authors' cited 'in preparation' paper is the missing load-bearing element.
  • The 7.5 TeV boundary is an extrapolation from a scan truncated at M1/2 = 5500 GeV; an extended scan might reveal the trend continues or that the top-mass constraint allows slightly different masses, so the exact boundary should be treated as indicative.
  • The same dilution mechanism, if confirmed, would apply to other SUSY models with overproducing neutralino dark matter, but only F-SU(5) ties it to a specific flaton sector; testing lambda6 through neutrino masses or lepton-flavor violation could provide independent checks.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper revisits No-Scale F-SU(5), a flipped SU(5) GUT with extra vector-like multiplets, after the LHC Run 2 gluino exclusion limit of 2.25 TeV. The authors abandon the usual upper limit on the neutralino relic density, scan the unified gaugino mass M1/2 from 1200 to 5500 GeV together with the vector-like mass scale MV, tanβ, and the top quark mass Mt, and require only the light Higgs mass in 124–127 GeV and the No-Scale Bμ = 0 condition. They find a gluino mass up to about 7.5 TeV and an LSP neutralino mass up to about 1.6 TeV, with the top quark mass still within its world-average range, and they argue that the resulting overproduction of dark matter can be diluted by the λ6 'master coupling' through late flaton decay. The paper presents a dozen benchmark spectra, checks flavor observables (b→sγ, Bs→μ+μ−, Δaμ), and reports that all benchmarks pass these constraints.

Significance. If the central claims hold, this would be a notable result: a natural, no-scale SUSY GUT with one dominant mass parameter could evade the LHC gluino bound without electroweak fine-tuning, while remaining consistent with the measured Higgs and top masses. The paper's strengths include explicit benchmark spectra, a transparent statement that the quoted relic densities are pre-dilution, and numerical checks of flavor observables with standard tools (SuSpect 2.34, MicrOMEGAs 2.1). The qualitative physics — that raising M1/2 raises the stop mass and hence Mh, requiring a lower Mt to stay in the 124–127 GeV window — is credible and visible in Fig. 2. However, the paper's cosmological viability claim for the heavy-gluino region depends on an imported λ6 dilution mechanism that is not computed here; this is the main load-bearing gap.

major comments (3)
  1. [§3 (The Master λ6 Coupling) and Table I] The central cosmological claim is not supported by a calculation in this paper. Table I explicitly lists the relic density as 'before dilution' and, for the heaviest benchmark (M1/2 = 5350 GeV), gives Ωχh² = 25.82, which requires an entropy dilution factor Δ ≈ 215 to reach Ωh² ≈ 0.12; the paper quotes Δ up to O(10^4) from refs [23,53], but no λ6 value, no point-by-point Δ, and no check of consistency with neutrino masses, baryogenesis, BBN, or gravitino overproduction is presented for any benchmark. Because the text states that the same λ6 determines neutrino masses and mixing, Δ cannot be treated as a free parameter; the paper must demonstrate that an allowed λ6 yields the required dilution for at least the benchmarks above the 2.25 TeV gluino exclusion. Without this, every point with Mg ≳ 2.3 TeV overcloses the universe if the dilution mechanism fails.
  2. [§4 (Analytical Procedure) and Fig. 2] The headline bound M(gluino) ≲ 7.5 TeV is an extrapolation, not the result of a scan that reaches the boundary. The scan is capped at M1/2 = 5500 GeV, which already corresponds to Mg ≈ 7.1 TeV at the heaviest benchmark in Table I, and the text concedes that extending the upper M1/2 limit would add points at large M1/2 and small Mt. Since the boundary is defined by the intersection of the Mh constraint with the Mt world-average band, the exact crossing should be established by scanning beyond the cap, or the claim should be rephrased as an approximate trend rather than an upper bound.
  3. [§4 (Analytical Procedure)] The scan floats Mt from 169 to 178 GeV, far outside the PDG world average of 173.1 ± 0.9 GeV, and the final consistency statement refers to a specific subset of points. The location of the 7.5 TeV boundary depends on this chosen Mt window; a wider or differently centered window would shift the boundary. Please clarify how the floated range is used in the scan versus the final presentation of consistency with the world-average top mass, and quantify the sensitivity of the boundary to the Mt window.
minor comments (5)
  1. [Table I and §3] Please define the dilution factor Δ explicitly, for example Δ = Ω_pre/Ω_target, and list the required Δ for each benchmark in Table I; currently only the pre-dilution abundances are given.
  2. [References [23,53]] Reference [53] is marked 'in preparation'; the paper should either cite a published version of the λ6 cosmology work or state explicitly that the dilution calculation is forthcoming and not part of this analysis.
  3. [Table I–Fig. 1 region] The text between Table I and Fig. 1 contains a long run of character sequences (e.g., '/s49 /s46 /s53...') that appear to be rendering artifacts; please check the source file and clean the compiled version.
  4. [Fig. 2 caption] Please describe in the caption what the colors or symbols denote (points satisfying 124 ≤ Mh < 127 GeV versus points failing the Higgs constraint) and what the dashed lines delimit beyond the top mass band.
  5. [§4 (Analytical Procedure)] The paper states that approximately 25 million points were scanned but does not specify whether this is a grid or random scan and what the density in M1/2, MV, tanβ, and Mt is; this information is needed to interpret the sparseness at the edges of Fig. 2.

Circularity Check

1 steps flagged · score 4.0 of 10

Heavy-gluino mass cap is a genuine scan result; dark-matter dilution is imported from the authors' λ6 papers, one in preparation.

  1. self citation load bearing [Abstract; Section 'The Master λ6 Coupling'; Table I caption; Refs. [23], [53]]
    "In order to dilute the relic density down to the WMAP and Planck measurements, we rely upon a single cosmological master coupling λ6. ... The Table I relic density consists of the calculated abundance for only the LSP, before dilution by the cosmological master coupling λ6. ... The decay of the flaton generates a second period of reheating where the amount of entropy released by the flaton decay Δ may be as big as O(10^4)."

    The claimed Ωh²≈0.12 consistency for the heavy-gluino points is not computed here: Table I gives only pre-dilution abundances (up to 25.82), and no λ6, entropy-release Δ, or per-benchmark dilution check is shown. The entire region with M(gluino)≳2.3 TeV depends on the λ6 mechanism reducing these abundances by up to about 200 while satisfying the same coupling's neutrino-mass, baryon-asymmetry, and gravitino constraints. Feasibility is asserted by citing Ref. [23] and Ref. [53] — the latter explicitly 'in preparation' — both from the same group, with Nanopoulos a co-author here. Thus the dark-matter consistency claim reduces to a self-citation chain. The 7.5 TeV gluino boundary itself is an independent, non-circular scan result, so the circularity is partial.

full rationale

Score 4 rather than higher because the headline gluino and LSP mass bounds are not circular: they follow from scanning the model and applying the independently measured Higgs-mass window (124 ≤ Mh < 127 GeV) and world-average top-quark mass range (Mt = 173.1 ± 0.9 GeV), and the paper explicitly discloses the M1/2 ≤ 5500 GeV scan cap, noting that extending it would densify but not change the trend. The problematic step is the dark-matter side. Every benchmark above the 2.25 TeV gluino exclusion has a pre-dilution Ωχ01h² larger than the measured value, by factors up to about 200; the paper does not compute λ6 or the entropy-dilution factor Δ for any benchmark, nor does it verify that a single allowed λ6 can provide the needed dilution while also producing the measured neutrino masses/mixing and baryon asymmetry. Instead it relies on the λ6 mechanism from Ref. [23] and Ref. [53], the latter marked 'in preparation', both involving overlapping authorship. That makes the model's consistency with the observed dark-matter abundance a load-bearing import from the authors' own prior and forthcoming work rather than a demonstrated prediction in this paper. Because the gluino-mass content is independently derived and the paper is transparent about the delegation, the appropriate score is 4 rather than a higher value.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The model supplies M1/2, MV, tan beta, and Mt as scanned inputs; the no-scale boundary conditions and the two-stage unification structure are inherited from earlier papers by the same group, and the lambda6 dilution mechanism that re-instates the dark matter constraint is imported from companion papers, one of which is in preparation. No new entities are postulated in this paper itself. The central bound therefore rests partly on input choices (Mt float range, scan cap, Mh window) and on an unquantified cosmological mechanism.

free parameters (5)
  • M1/2 (unified gaugino mass) = Scanned over 1200 to 5500 GeV.
    Single SUSY-breaking parameter of the no-scale model; all soft masses scale with it at leading order. The headline 7.5 TeV gluino bound is the edge of the scanned range, not a fitted value.
  • MV (flippon decoupling scale) = Scanned over 10 to 1500 TeV; benchmark values up to 1.15e6 GeV.
    Free vector-like mass scale in F-SU(5), scanned per benchmark; Table I shows it varying across two orders of magnitude, so the 'one-parameter' framing does not apply to the scan.
  • tan beta = Scanned over 2 to 50; surviving points 9 to 25.
    In principle fixed by Bmu = 0, implemented by floating tan beta and keeping points with |Bmu| less than or equal to 1 GeV at MF.
  • Mt (top quark mass input) = Scanned from 169 to 178 GeV; benchmarks 172.4 to 173.8 GeV.
    Floated beyond the measured 173.1 plus or minus 0.9 GeV band; the gluino ceiling is set by where Mt leaves the world-average range, so the bound depends on how far Mt is allowed to float.
  • lambda6 master coupling and entropy dilution Delta = Not specified; needed dilution up to about 215, claimed possible up to O(10^4).
    The cosmological dilution factor is invoked from refs [23,53] to restore Omega h^2 of about 0.12; no lambda6 value, neutrino-mass check, or point-by-point dilution is computed in this paper.
assumptions (7)
  • domain assumption The no-scale SUGRA boundary conditions M0 = A0 = Bmu = 0 apply at the string scale MF of about 2 times 10^17 GeV.
    This defines the model and is inherited from refs [16,17,40,41]; it is stated, not re-derived, in Section II.
  • domain assumption Bmu = 0 is strictly enforced as |Bmu| less than or equal to 1 GeV at MF.
    Used to select tan beta values; stated in Section III ('Analytical Procedure').
  • domain assumption Two vector-like flippon multiplets at a common scale MV realize string-scale unification with b3 = 0 and two-stage unification at M32 and MF.
    Model structure inherited from refs [12,14,15,17]; MV is left free in the scan.
  • domain assumption The proprietary SuSpect 2.34 modification and MicrOMEGAs 2.1 correctly implement the enhanced F-SU(5) RGEs and relic-density calculations.
    Numerical pipeline stated in Section III; no code or validation data is shipped.
  • domain assumption The lambda6 flaton-decay mechanism can dilute the relic density by up to about 10^4, as claimed for the lambda6 universe.
    Load-bearing for the dark-matter constraint; imported from refs [23,53], with ref [53] listed as in preparation. Section IV does not compute the dilution for the benchmark points.
  • ad hoc to paper The top quark mass may be floated to 169 to 178 GeV, beyond the PDG world average of 173.1 plus or minus 0.9 GeV, to keep Mh within 124 to 127 GeV.
    The gluino ceiling is set by where Mt would leave the world-average band, so the headline bound depends on this float range.
  • domain assumption The practical constraint on the light Higgs mass is 124 to 127 GeV, combining 2-sigma experimental and about 1.5 GeV theoretical uncertainty.
    Stated in Section III; the 7.5 TeV boundary depends on this chosen window.

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Cite this review

Pith. "Pith review of The Heavy Gluino in Natural No-Scale $\cal{F}$-$SU$(5)." pith.science (2026). https://pith.science/paper/ST5QPJZJ

@misc{pith2026190806149,
  author       = {Pith},
  title        = {Pith review of: The Heavy Gluino in Natural No-Scale $\calF$-$SU$(5)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ST5QPJZJ}},
  note         = {Machine review of arXiv:1908.06149}
}
abstract

In light of recent 80-137 $\rm{fb}^{-1}$ results at the LHC Run 2 establishing a lower gluino mass limit of 2.25 TeV, we revisit the supersymmetric GUT model Flipped $SU$(5) with extra vector-like particles, known as $\cal{F}$-$SU$(5), with vanishing No-Scale Supergravity boundary conditions at the string scale of about $2 \times 10^{17}$ GeV, including the supersymmetry breaking $B_{\mu}$ parameter which is strictly enforced as $B_{\mu} = 0$. Given the proportional dependence of all model scales on a single parameter $M_{1/2}$, No-Scale $\cal{F}$-$SU$(5) was shown to possess no electroweak fine-tuning and thus persists as a $natural$ one-parameter model. In this fresh analysis here, we demand consistency with the measured 125 GeV light Higgs boson mass, though we forgo an upper limit on the lightest neutralino relic density. The resulting phenomenology delivers a gluino mass of $M(\widetilde{g}) \lesssim 7.5$ TeV and a lightest supersymmetric particle (LSP) of $M(\widetilde{\chi}_1^0) \lesssim 1.6$ TeV. In order to dilute the relic density down to the WMAP and Planck measurements, we rely upon a single cosmological master coupling $\lambda_6$.

Figures

Figures reproduced from arXiv: 1908.06149 by the authors.

Figure 1
Figure 1. FIG. 1: Depiction of SUSY spectrum masses for the LSP [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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