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Implications of Higgs mass for hidden sector SUSY breaking

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Pith's one-line read The paper argues that the measured 125 GeV Higgs mass, taken with electroweak naturalness and string-landscape statistics, favors gravity-mediated supersymmetry breaking with hidden-sector singlets over charged-hidden-sector PeV or…

desk verdict A clean, conditional argument that m_h ~ 125 GeV plus a landscape prior favors singlet hidden-sector gravity mediation; the numerics are solid, but the probabilistic punchline rests on the authors' prior, not re-derived here. read the letter →

arxiv 2412.15356 v2 pith:IPAGGITF submitted 2024-12-19 hep-ph

Howard Baer , Vernon Barger , Jessica Bolich , Kairui Zhang This is my paper · ORCID
classification hep-ph
keywords supersymmetryHiggsbosonmassnaturalnesselectroweakfine-tuninggravitymediationhiddensectorPeV-scaleSUSYstringlandscape
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

The paper argues that the measured Higgs mass $m_h \simeq 125$ GeV, combined with electroweak naturalness and a string-landscape preference for natural models, selects how supersymmetry is broken in the hidden sector. Models with charged hidden-sector fields give loop-suppressed trilinear soft terms, so reaching the measured Higgs mass forces top squarks into the 10-100 TeV range and makes the weak scale highly fine-tuned. Gravity-mediated models with hidden-sector gauge singlets instead generate large $A$-terms, lifting $m_h$ to 125 GeV with stops near 1-3 TeV and $\Delta_{\rm EW} \lesssim 30$. If the argument is right, PeV-scale and mini-split SUSY are strongly disfavored, and the expected realization of weak-scale SUSY involves singlet-driven gravity mediation.

What carries the argument

The load-bearing identity is the MSSM light-Higgs mass formula $$$m_h^{2}$ \simeq $m_Z^{2}$ \$cos^{2}$ 2\$\beta$ + \frac{$3g^{2}$ $m_t^{4}$}{8\$pi^{2}$ $m_W^{2}$}\left[\log\frac{m_{\rm SUSY}^2}{$m_t^{2}$} + \frac{$x_t^{2}$}{m_{\rm SUSY}^2}\left(1-\frac{$x_t^{2}$}{12 m_{\rm SUSY}^2}\right)\right],$$ with $x_t = A_t - \mu\cot\beta$. Because $m_h$ is maximized near $x_t = \pm\sqrt{6}\,m_{\rm SUSY}$, the measured value 125 GeV forces either multi-10-TeV stops at small $A_t$ or TeV-scale stops with large $A_t$. The companion machinery is the electroweak fine-tuning measure $\Delta_{\rm EW}$, defined as the largest term on the right-hand side of Eq. (1) divided by $m_Z^2/2$; top-squark loop contributions $\Sigma_u^u(\tilde t_{1,2})$ grow roughly as $m_{\tilde t}^2/16\pi^2$, so multi-10-TeV stops make $\Delta_{\rm EW}$ huge, while TeV-scale stops with large $A_t$ remain natural.

What would settle it

The decisive check is a full two-loop calculation of $\Delta_{\rm EW}$ for a charged-hidden-sector spectrum with small $A_t$ and stops around 10-100 TeV that reproduces $m_h \simeq 125$ GeV; if any such point yields $\Delta_{\rm EW} \lesssim 30$, the naturalness argument against PeV-scale or mini-split SUSY fails. The opposite confirmation would be a future measurement finding stops near 1-3 TeV with large $A_t$ and light higgsinos.

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Extended reading notes

Core claim

On its own terms, the paper establishes a three-step chain. Within the MSSM, $m_h \simeq 125$ GeV requires either 10-100 TeV top squarks with small $A_t$, or TeV-scale top squarks with large trilinear terms near the maximal-mixing value $x_t = A_t - \mu\cot\beta \simeq \pm\sqrt{6}\,m_{\rm SUSY}$. Charged hidden-sector SUSY breaking produces the small-$A_t$ situation, with scalar masses roughly $16\pi^2$ times gaugino masses, so reproducing the measured Higgs mass forces scalars into the 10-100 TeV range, where the $\Sigma_u^u(\tilde t_{1,2})$ contributions make $\Delta_{\rm EW}$ enormous. Gravity mediation with a hidden-sector gauge singlet produces $m_{\rm scalar} \sim m_{\rm gaugino} \sim A_t$, so large $A_t$ lifts $m_h$ to 125 GeV with stops near 1-3 TeV and $\Delta_{\rm EW} \lesssim 30$. The paper concludes that the measured Higgs mass most plausibly points to singlet hidden sectors, as in metastable and retrofitted dynamical SUSY breaking, and against PeV-scale or mini-split spectra.

Load-bearing premise

The conclusion stands or falls on the premise that the string landscape statistically favors models with a naturally small weak scale over fine-tuned ones by a large volume factor; if that prior is wrong, or if $\Delta_{\rm EW}$ is not the right measure of naturalness, the measured Higgs mass alone does not single out hidden-sector singlets.

Editorial extensions

If this is right

  • Charged-hidden-sector models such as PeV-scale and mini-split SUSY require 10-100 TeV scalars to give $m_h \simeq 125$ GeV and are therefore disfavored by electroweak naturalness.
  • Singlet gravity mediation predicts $m_{\rm scalar} \sim m_{\rm gaugino} \sim A_t$, with stops in the few-TeV range and higgsinos around 100-350 GeV, so the lightest SUSY particle is typically higgsino-like.
  • Landscape volume arguments place fine-tuned mini-split and PeV models at relative probabilities around $10^{-4}$ to $10^{-8}$ compared with natural models.
  • Natural spectra can still have gluinos up to about 6-9 TeV, so current collider gluino limits do not exclude the favored singlet scenario.
  • Hidden-sector effects such as scalar sequestering do not rescue small-$A_t$ models, since 10-100 TeV stops still generate large $\Sigma_u^u$ contributions to the weak scale.

Reading between the lines

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

  • If the string-landscape prior holds up, the measured Higgs mass becomes an indirect probe of hidden-sector field content, and a natural-spectrum discovery with large $A_t$ would corroborate singlet-driven gravity mediation.
  • A future collider measuring the stop mass and $A_t$ together could directly separate the two hidden-sector structures, because singlet gravity mediation predicts large $A_t$ at fixed stop mass while charged hidden sectors predict near-zero $A_t$.
  • The same logic extends to non-minimal Higgs sectors such as NMSSM or vector-like matter, which raise $m_h$ without large $A_t$; whether those evade the conclusion depends on how their extra states enter $\Delta_{\rm EW}$.
  • If the favored scenario is correct, the LHC should first see higgsino-like missing-energy signatures, while squark and gluino signals may remain beyond reach.
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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 / 6 minor

Summary. This paper argues that the measured Higgs mass m_h ≈ 125 GeV, combined with the electroweak naturalness measure ΔEW and a string-landscape prior, favors gravity-mediated SUSY breaking with hidden sector gauge singlets over charged-hidden-sector dynamical SUSY breaking (PeV/mini-split). The authors compute m_h as a function of A_t for an NUHM2 benchmark, demonstrate that models with small A-terms (GMSB, inoMSB, charged SUSY breaking) require stop masses of 10-100 TeV to reach m_h ≈ 125 GeV, and show that such heavy stops generate large ΔEW values. They present NUHM2 parameter planes with A0 = -1.6m0 where the natural (ΔEW < 30) region has m_h in the 123-127 GeV range, and conclude that the measured Higgs mass points to singlet hidden sectors because natural models are statistically preferred by the landscape.

Significance. If established, the paper would forge a direct link between the measured Higgs mass and the statistical structure of the string landscape, with significant implications for hidden sector model building. The m_h-A_t relation is standard, and the numerical analysis uses established codes (Isajet/FeynHiggs); the explicit consideration of hidden-sector running in Section 4 is a strength. However, the central probabilistic conclusion rests on two contested assumptions—the ΔEW naturalness measure and the landscape prior imported from Refs. [84,85]—neither of which is re-derived or stress-tested here. The paper's significance is therefore conditional on these priors, but the underlying physics discussion is informed and the conclusions are clearly drawn.

major comments (3)
  1. [Section 3.2, paragraph citing Refs. [84,85]] The decisive quantitative input—that fine-tuned PeV-SUSY/mini-split models are suppressed relative to natural models by probabilities of 10^-4 to 10^-8—is imported from Refs. [84,85] rather than derived in this manuscript. Because those references are earlier works by the same group, and because the landscape measure is sensitive to choices such as the prior on soft parameters (uniform in m0 vs. uniform in log m0), the definition of the ABDS window, and the counting of vacua, the reader cannot assess the robustness of this input from the present paper. The manuscript should either provide a self-contained derivation of the relative probabilities or explicitly analyze the measure dependence and state which conclusions survive. As written, the abstract-level claim that m_h favors hidden sector singlets is conditional on an unvalidated prior.
  2. [Eq. (2) and Figs. 4-5] The conclusion that charged-hidden-sector models are unnatural and hence disfavored rests on the ΔEW measure with an implicit threshold ΔEW < 30. The paper defends ΔEW against Δ_pi and Δ_HS in footnote 1, but it does not show that the central conclusion is robust to the choice of naturalness measure or to the threshold value. This is especially important because the landscape prior argument is itself measure-dependent; a prior on high-scale parameters or a different naturalness criterion could eliminate the suppression of heavy stops and undo the selection of singlet hidden sectors. Please provide an explicit sensitivity check or qualify the conclusion accordingly.
  3. [Fig. 5 and Section 3.2] The natural NUHM2 region with m_h ≈ 125 GeV is exhibited for a single A0 ratio, A0 = -1.6m0, and the text does not quantify how this region shrinks or shifts for other A0 values. Since the landscape prior is a distribution over A0, the paper should show the A0-dependence of the natural m_h-allowed region or provide a statistical argument that this ratio is favored. Without this, the claim that the singlet hidden sector case 'largely has 123 GeV < m_h < 127 GeV' in the natural region is not fully demonstrated.
minor comments (6)
  1. [Section 3.2] The phrase 'bourne out' should read 'borne out'.
  2. [Eq. (4) and Figs. 1-2] Use consistent notation for the trilinear coupling: define A_t once and use it throughout (the text alternates between 'At', 'A_t', and 'A_t(weak)').
  3. [Section 2.1.1] The formula for scalar masses in GMSB, written as 'm2_i ∼ (αi/4π Λ)^2', is ambiguous; please rewrite as m_i^2 ∼ (α_i/4π)^2 Λ^2 (or with explicit parentheses) to avoid confusion.
  4. [References] Reference [73] for the Polonyi superpotential is incomplete; please provide a full citation or a reference to a published source.
  5. [Section 1 and footnote 1] Fix the typesetting of 'Δ_pi' and 'Δ_HS' in footnote 1, and correct the inline 'mweak ∼ msof t∼ m2 hidden/mP' to use proper subscripts.
  6. [Figs. 2 and 4 captions] Specify in the captions which curves are m_h (theory) and which are ΔEW, and note that the m_h uncertainty is taken as ±2 GeV in the text but not shown on the figures.

Circularity Check

1 steps flagged · score 4.0 of 10

Verdict: the m_h/stop/A_t computation is independent and standard, but the key probabilistic step that disfavors PeV/mini-split SUSY is imported from the same authors' landscape analyses Refs. [84,85].

  1. self citation load bearing [Section 3.2 (Singlet SUSY breaking fields), paragraph invoking Refs. [84,85]; echoed in Section 5 Conclusions]
    "This is bourne out in Ref. [84] where natural SUSY models– with all contributions to the weak scale being comparable to the weak scale– have a far larger volume of parameter space on the landscape than finetuned models. ... For instance, in Ref. [85] it is found that certain finetuned models of mini-split or PeV-SUSY occur at probabilities of ∼ 10−4 − 10−8 with respect to natural models, based on the volume of parameter space on the landscape."

    The advertised inference is: m_h forces large A_t or 10-100 TeV stops; the latter are unnatural; unnatural models have tiny landscape volume; therefore singlets are favored. The first two steps are independent physics, but the third step, including the quantitative 10^-4 to 10^-8 suppression, is taken verbatim from the same authors' earlier Refs. [84,85] and is not re-derived, benchmarked, or shown to be measure-independent in this paper. Without that imported landscape prior, the identical m_h computation and Delta_EW analysis would not by themselves attach a probability ratio to charged hidden sector models; a different but equally plausible landscape measure could restore their viability.

full rationale

The core Higgs-mass content of the paper is self-contained and non-circular: Eq. (4) is the standard MSSM Higgs-mass formula, the Delta_EW measure in Eqs. (1)-(3) is explicit, and the m_h vs. At and A0 plots are generated with the independent external codes Isajet and FeynHiggs. The observation that small A_t requires 10-100 TeV stops to reach m_h ~ 125 GeV is a well-known consequence and is not fitted to the paper's conclusion. The circularity-analogous step is located in the probabilistic layer: the paper's strong claim that PeV/mini-split models are disfavored by 10^-4 to 10^-8 relative to natural SUSY relies on Refs. [84,85], which are prior papers by the same group and which are not re-derived or independently validated here. The m_h measurement alone does not algorithmically produce that probability ratio; the ratio comes from a specific landscape prior. Since the central claim still contains substantial independent MSSM/Higgs content and the self-citation is not definitionally forced, the score is 4 rather than higher. No fitted input is renamed as a prediction, and no uniqueness theorem is fabricated; the weakness is a load-bearing but unverified self-citation at the landscape-probability step.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a few domain assumptions: the Delta_EW naturalness measure, the landscape prior (self-cited), the validity of the MSSM EFT between mGUT and mweak, and the reliability of Isajet/FeynHiggs calculations. The scanned benchmark values are chosen by hand and shape the plotted natural regions. No new entities are introduced.

free parameters (4)
  • benchmark mu = 200 GeV = 200 GeV
    Chosen for naturalness in NUHM2 and CSB plots; the natural regions and Delta_EW contours depend on this value.
  • benchmark mA = 2 TeV = 2 TeV
    Fixed in Figs 1, 2, 4b, 5; affects the Higgs sector and the plotted contours.
  • benchmark tan beta = 10 = 10
    Used in all main scans; tan beta enters the Higgs mass formula and the Delta_EW measure.
  • A0 = -1.6 m0 = -1.6 m0
    Chosen in the NUHM2 scan to be near maximal mixing; the claimed natural mh=125 GeV region depends on this choice.
assumptions (4)
  • domain assumption The electroweak fine-tuning measure Delta_EW, defined as the maximum term in Eq. 1 divided by mZ^2/2, is the appropriate measure of naturalness.
    The paper's central comparison of charged vs. singlet hidden sectors is conducted on this measure. See Eq. 2 and the discussion after it.
  • ad hoc to paper The string landscape statistically favors models with a natural weak scale, with quantitative probability statements from Refs [84,85].
    The paper cites its own prior work for the claim that natural models have far larger landscape volume than fine-tuned ones; this is a contested hypothesis rather than an established fact. Invoked in Section 3.2.
  • domain assumption The MSSM is the valid low-energy EFT between mGUT and mweak, and hidden sector running effects on visible soft terms are negligible.
    Stated in Section 4 as an implicit assumption and defended against scalar sequestering scenarios, which would modify the mHu, mHd correlation used in Eq. 1.
  • standard math The mass spectrum calculations from Isajet and FeynHiggs are reliable, with a theory uncertainty of +/-2 GeV on mh.
    All plots use these codes and the allowed mh band 123-127 GeV. This is a standard tooling assumption for MSSM spectra.

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Cite this review

Pith. "Pith review of Implications of Higgs mass for hidden sector SUSY breaking." pith.science (2026). https://pith.science/paper/IPAGGITF

@misc{pith2026241215356,
  author       = {Pith},
  title        = {Pith review of: Implications of Higgs mass for hidden sector SUSY breaking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPAGGITF}},
  note         = {Machine review of arXiv:2412.15356}
}
read the original abstract

Hidden sector SUSY breaking where charged hidden sector fields obtain SUSY breaking vevs once seemed common in dynamical SUSY breaking (DSB). In such a case, scalars can obtain large masses but gauginos and A-terms gain loop-suppressed anomaly-mediated contributions which may be smaller by factors of 1/16\pi^2 ~1/160. This situation leads to models such as PeV or mini-split supersymmetry with m(scalars)~ 160 m(gauginos). In order to generate a light Higgs mass m_h~ 125 GeV, the scalar mass terms are required in the 10-100 TeV range, leading to large, unnatural contributions to the weak scale. Alternatively, in gravity mediation with singlet hidden sector fields, then m(scalars)~ m(gauginos)~ A-terms and the large A-terms lift m_h ->125 GeV even for natural values of m(stop1)~ 1-3 TeV. Requiring naturalness, which is probabilistically preferred by the string landscape, then the measured Higgs mass seems to favor singlets in the hidden sector, which can be common in metastable and retrofitted DSB models.

Figures

Figures reproduced from arXiv: 2412.15356 by the authors.

Figure 1
Figure 1. Value of mh vs. At(weak) from FeynHiggs for the NUHM2 model with m0 = 5 TeV, m1/2 = 1.2 TeV, A0 = −8 TeV tan β = 10, µ = 200 GeV and mA = 2 TeV. For reference, in Fig. 2a) we plot the value of mh for the same NUHM2 benchmark point as in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. In a), we show the value of mh vs. A0 from FeynHiggs and Isasugra for the NUHM2 model with m0 = 5 TeV, m1/2 = 1.2 TeV, tan β = 10, µ = 200 GeV and mA = 2 TeV. Frame b) shows the difference in mh between FeynHiggs and Isasugra. • again within the MSSM, one can have TeV-scale top-squarks but with large A-terms [35] or • one may proceed beyond the MSSM and add additional fields, such as NMSSM singlets 4 [PITH_FULL_IMA… view at source ↗
Figure 3
Figure 3. Plot of a) mh (left vertical axis, blue curve) and ∆EW (right vertical axis, red curve) vs. m1/2 in the inoMSB model for tan β = 10 and µ > 0. In frame b), we plot several sparticle masses vs. m1/2. SUGRA operators. Scalar masses arise from terms such as Z d 4 θcij X†XQ† iQj m2 P → cij F † XFX m2 P ϕ ∗ i ϕj (5) where the X fields are hidden sector SUSY breaking fields and the Q are visible sector chiral superfields … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Parameter space of charged SUSY breaking (CSB) model with [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Parameter space of the singlet sector gravity-mediation model NUHM2 in the [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Pith tools

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