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Supersymmetry and LHC era

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Pith's one-line read SUSY can still explain the muon g-2 anomaly in the LHC era

desk verdict A competent, up-to-date review of SUSY after the LHC, but its central g-2 benchmark scenario depends on an unquantified proton-decay suppression factor. read the letter →

arxiv 2505.01769 v1 pith:UO37C3XA submitted 2025-05-03 hep-ph hep-th

Hyun Min Lee This is my paper · ORCID
classification hep-phhep-th
keywords supersymmetryMSSMmuong-2anomalyLHCsuperpartnersearchesgeneralgaugemediationprotondecayWbosonmassHiggs
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 review argues that supersymmetry is not dead after the LHC: the stringent bounds on gluinos and squarks push the colored superpartners to multi-TeV masses, but the discrepancy in the muon's magnetic moment can still be explained by relatively light electroweak superpartners: sleptons, electroweak gauginos, and Higgsinos. The paper shows this is achievable in general gauge mediation, where the SUSY-breaking messenger sector can produce split masses with heavy squarks and light sleptons. It also connects the same framework to the $W$ boson mass, the 125 GeV Higgs mass, and proton decay in SU(5)-type unification. The reader is left with a concrete, testable picture: if the muon $g-2$ anomaly persists, the LHC searches to watch are prompt and displaced decays of sleptons, charginos, and neutralinos.

What carries the argument

The argument runs on one-loop corrections computed from the MSSM Lagrangian. The slepton contributions to the muon magnetic moment come from chargino--sneutrino loops ($a^{(1)}_\mu$) and neutralino--smuon loops ($a^{(2)}_\mu$), whose signs and sizes depend on $\tan\beta$, $\mu_H$, the gaugino masses $M_1$, $M_2$, and smuon mixing. The same slepton mass splittings feed the $\rho$ parameter and hence shift the $W$ mass. Proton decay is controlled by effective dimension-five operators generated when colored Higgsinos are integrated out; the estimate $\tau(p\to K^+\bar\nu) \simeq 4\times 10^{35}\,\text{yr}\times \sin^4 2\beta\,(\cdots)\,(M_{H_C}/\kappa /10^{16}\,\text{GeV})^2$ ties squark, stop, and stau masses to the proton lifetime bound and is the concrete object that makes the scenario falsifiable.

What would settle it

A decisive test is the comparison between the final experimental value of $a_\mu$ and a lattice-QCD-based Standard Model prediction: if they agree within about $1\sigma$, the anomaly vanishes and the benchmark spectra built to produce $\Delta a_\mu\simeq 249\times 10^{-11}$ would address no known discrepancy.

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Extended reading notes

Core claim

The paper's central claim is that, despite LHC exclusions of gluinos up to about 2.4 TeV and squarks up to about 1.8 TeV, the Minimal Supersymmetric Standard Model remains viable as an explanation of the muon $g-2$ anomaly. The required spectrum is split: colored superpartners sit at multi-TeV masses, while sleptons, Binos, Winos, and Higgsinos stay near the electroweak scale. In benchmark models drawn from general gauge mediation, one-loop slepton contributions produce $\Delta a_\mu$ within 1--2$\sigma$ of the measured discrepancy, and one model simultaneously fits the high-precision $W$ boson mass measurement. The review further argues that proton decay through dimension-five operators, normally a serious problem for supersymmetric SU(5), can be suppressed by small colored-Higgsino Yukawa couplings ($\kappa \sim 10^{-4}$--$10^{-3}$), as realized in orbifold GUTs, bringing the predicted proton lifetime above the current experimental bound.

Load-bearing premise

The load-bearing premise is that the muon $g-2$ anomaly is real, meaning the Standard Model prediction obtained from the $e^+e^-$ dispersive approach is the correct benchmark; the paper itself notes that lattice QCD and recent cross-section results are consistent with experiment, and if those results win out, the $5.2\sigma$ discrepancy that motivates its benchmark models disappears.

Editorial extensions

If this is right

  • If the $g-2$ explanation is correct, the discovery targets at the LHC are electroweak superpartners: sleptons up to roughly 700 GeV and charginos or heavier neutralinos up to about 1.2 TeV in prompt searches, with displaced-vertex searches covering the long-lived LSP cases.
  • The same parameter space predicts a $W$ boson mass shift from slepton contributions to the $\rho$ parameter, so a future high-precision $W$ mass measurement can discriminate among the benchmark models.
  • The proton lifetime bound turns into a constraint on GUT structure: minimal SU(5) with TeV-scale superpartners is excluded unless $\kappa$ is suppressed to roughly $10^{-4}$--$10^{-3}$, pointing toward orbifold GUTs.
  • If the muon $g-2$ anomaly is resolved by lattice QCD or the recent cross-section data, the electroweak superpartners no longer need to be light, and the remaining SUSY constraints are the Higgs mass and proton lifetime.
  • Searches for stau pair production can test the flavor universality of slepton masses assumed in the benchmark models, indirectly probing the proton lifetime prediction.

Reading between the lines

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

  • A hidden implication is that naturalness has quietly dropped out of the argument: multi-TeV squarks already force fine-tuning, so the case for supersymmetry now rests on explaining measured anomalies rather than stabilizing the weak scale.
  • The same split-spectrum logic is highly adaptable: any future electroweak anomaly could be fit by light electroweak superpartners without disturbing the heavy colored sector, making the framework harder to falsify.
  • The reliance on a small $\kappa$ suggests a testable connection: if orbifold-GUT wavefunction suppression is why proton decay is slow, the same suppression should appear in other GUT predictions, such as Yukawa unification relations.
  • A future collider measuring slepton masses in the 100--500 GeV range, combined with an improved $W$ mass measurement, could distinguish the three benchmark models in a way current searches cannot.
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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

2 major / 6 minor

Summary. The manuscript is an invited review of supersymmetry in the LHC era. It recapitulates the MSSM field content, R-parity, soft terms, the tree-level Higgs-mass bound, and the stop-loop correction to the Higgs quartic, then summarizes current ATLAS/CMS limits on gluinos, squarks, stops, and electroweak superpartners. It derives the slepton-loop contributions to the W mass and muon g−2, presents three general gauge mediation benchmark models from the author's prior work that fit the muon g−2 anomaly (and, in one case, the CDF-II W mass), and reviews dimension-five proton decay in minimal SU(5), quoting the Super-K limit and estimating lifetimes as functions of the squark mass and the colored-Higgsino suppression factor κ. The conclusions argue that light electroweak superpartners can accommodate the g−2 anomaly and that the proton-decay problem can be evaded by orbifold-GUT wavefunction suppression.

Significance. The review is a useful and largely accurate compendium for an encyclopedia article: the quoted LHC limits are current, the analytic formulas for the neutralino, chargino, and slepton spectra and for the g−2 contributions are given at an appropriate level of detail, and the paper is honest about two major caveats—the lattice-QCD and CMD-3 results may remove the muon g−2 anomaly, and the benchmark spectra are illustrative choices rather than predictions. Its main value is as a compact reference to the status of the MSSM parameter space after the LHC. As discussed below, however, the overall viability claim is conditional on a proton-decay suppression mechanism that is asserted but not demonstrated in the review.

major comments (2)
  1. [Section 5, Eq. (102); Conclusions] The claimed compatibility of the benchmark spectra with the proton-lifetime bound is not self-contained. The estimate requires a suppression factor κ∼10^-4–10^-3 for squark masses of order 3–7 TeV and sleptons near 100 GeV, but the review does not present or cite an explicit orbifold-GUT construction that naturally produces this value; it only states that tree-level colored-Higgsino Yukawa couplings can be forbidden at an orbifold fixed point. The concluding sentence that the problem 'can be solved' by orbifold GUTs should therefore be rephrased as a conditional claim, or backed by a concrete model, because the advertised viable parameter space disappears if κ is not that small.
  2. [Section 4.2 and Fig. 3] The benchmark models are selected from Ref. [23] to satisfy Δaμ and, for Model III, the CDF-II W-mass value, so their agreement with these observables is a fit rather than an independent prediction. The paper should state this explicitly, both near Fig. 3 and in the Conclusions, so that the wording 'can be accommodated' is not read as a predictive test of supersymmetry.
minor comments (6)
  1. [Section 4.2, text before Eq. (85)] The sentence 'There are two typos of supersymmetric interactions' should read 'two types of supersymmetric interactions'.
  2. [Eq. (28)] The soft mass term written as m^2_{~dc,ij}|~u_i^c|^2 should multiply |~d_i^c|^2 rather than |~u_i^c|^2.
  3. [Section 3, Eq. (35)] The sign of the quadratic divergence in the top-loop contribution appears opposite to the usual convention; please check the expression and correct it if needed.
  4. [Section 4.2, after Eq. (74)] The text refers to 'Appendix A' for the full neutralino and chargino mixing matrices, but no Appendix A appears in the manuscript; either include the appendix or remove the pointer.
  5. [Fig. 6 caption] The notation 'm_e = 250 GeV' should be written as m_{\tilde e_R} (or otherwise defined) to avoid confusion with the electron mass.
  6. [Figs. 4 and 5] The reproduced plots are quite small and the labels are difficult to read; larger fonts and higher resolution would help readers verify the quoted limits.

Circularity Check

2 steps flagged · score 6.0 of 10

Benchmark g−2 'predictions' are fit targets from the author's prior model, and proton-lifetime consistency is imposed by an unquantified κ.

  1. fitted input called prediction [Section 4.2, paragraph after Eq. (97) and Fig. 3 caption]
    "In the left of Fig. 3, we present three benchmark models which are consistent with the muon g−2 anomaly within 1σ (Model II and III) or 2σ (Model I) in general gauge mediation [23]. We listed the masses for electroweak superpartners in general gauge mediation and the predictions for ∆aµ and ∆MW. In particular, Model III is also consistent with the W boson mass measured by CDFII within 1σ."

    The benchmark spectra are selected so that the computed ∆aµ falls inside the 1σ or 2σ window of the experimental anomaly; the 'predictions for ∆aµ' are therefore the fit target re-expressed, not outputs of an independently fixed spectrum. Model III's consistency with the CDFII W mass is likewise imposed by the choice of spectrum. The Conclusion's statement that the SUSY explanation 'can be accommodated' is an existence claim demonstrated by this construction, but the agreement is by construction rather than a first-principles prediction.

  2. ansatz smuggled in via citation [Section 5, around Eq. (102) and Fig. 6; Conclusions, last paragraph]
    "For instance, for squark masses of order 3 − 7 TeV and the slepton masses of order 100 GeV required for the muon g− 2 anomaly, it is sufficient to take a suppression factor, κ∼ 10−4− 10−3, to satisfy the bound on the proton lifetime. ... the problem of the proton lifetime can be solved when the model is embedded in the orbifold GUTs where the Higgsino wavefunctions get suppressed at the orbifold fixed point, so do the dimension-5 operators for the proton decays."

    The proton-lifetime bound is satisfied only because κ is inserted by hand into Eq. (102) at the value needed for the g−2-favored light-slepton spectrum; no concrete orbifold GUT is specified that actually produces κ∼10−4–10−3. The only cited source for this suppression is the author's prior work [23], which treats κ as a chosen parameter rather than deriving it from an explicit extra-dimensional model. Thus the advertised consistency with proton decay is not a consequence of general gauge mediation or of a demonstrated GUT embedding; it is an ansatz imported into the conclusion.

full rationale

The paper is largely a review: the MSSM setup, Higgs-mass formulas, the W-mass analysis, and the LHC limits come from external experiment and standard references, and those parts are not circular. However, the central existence claim for light electroweak superpartners explaining the muon g−2 anomaly is supported by benchmark models taken from the author's prior work [23], and those benchmarks are explicitly constructed to be consistent with the anomaly. The 'predictions for ∆aµ' in Fig. 3 are therefore fit outputs, not independent predictions; the agreement is by construction. The proton-lifetime section likewise shows that the g−2-favored spectrum satisfies the Super-K bound only if a colored-Higgsino Yukawa suppression κ∼10−4–10−3 is assumed, with no concrete orbifold GUT realization given; the conclusion that the problem 'can be solved' in orbifold GUTs imports this ansatz rather than deriving it. The paper does honestly flag the lattice QCD and CMD-3 uncertainty in the anomaly and presents the LHC bounds as external, which keeps the circularity moderate rather than total.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper does not introduce new particles or forces; it reviews the MSSM, whose superpartners are established beyond-Standard-Model constructs. All free parameters are inherited from prior model-building and are tuned to satisfy the phenomenological constraints discussed in the review.

free parameters (6)
  • tanβ = 30
    Set to 30 in all benchmark models used in the review to enhance Yukawa contributions to the muon g-2; chosen to make the anomaly explanation work.
  • μH (Higgsino mass parameter) = 1200 GeV
    Chosen in the benchmark scenarios of Fig. 6 and Ref. [23] to balance chargino contributions and proton decay constraints.
  • m_eR (selectron mass) = 250 GeV
    Chosen for the proton lifetime plot in Fig. 6; represents light sleptons needed for the muon g-2 excess.
  • κ (dimension-5 operator suppression factor) = 1 down to 10^-4
    Varied to satisfy the Super-Kamiokande bound on p -> K+ nu; in orbifold GUTs it is assumed to be small.
  • N2, N3 (effective numbers of messenger fields)
    Used in general gauge mediation to fit the muon g-2 anomaly while respecting the proton lifetime bound.
  • M1 = M2/2 (gaugino masses) = 400 GeV
    Chosen in the right panel of Fig. 6 to fit the anomaly and proton lifetime constraints.
assumptions (5)
  • domain assumption R-parity is conserved in the MSSM
    Ensures the LSP is stable and a dark matter candidate; adopted without proof throughout the review.
  • domain assumption The MSSM matter fields embed into SU(5) representations 5-bar + 10
    Needed to generate dimension-5 proton decay operators; standard GUT assumption used in Section 5.
  • domain assumption General gauge mediation provides the soft SUSY breaking spectrum
    The review's benchmark models rely on this mechanism to split colored and non-colored superpartner masses.
  • domain assumption The SM prediction for the muon g-2 based on the dispersive approach is correct
    The anomaly is defined relative to this prediction; the paper itself notes lattice and CMD-3 data may differ.
  • standard math Colored Higgsinos are integrated out to produce dimension-5 operators
    Effective field theory integration used to derive proton decay amplitudes in Section 5.

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Cite this review

Pith. "Pith review of Supersymmetry and LHC era." pith.science (2026). https://pith.science/paper/UO37C3XA

@misc{pith2026250501769,
  author       = {Pith},
  title        = {Pith review of: Supersymmetry and LHC era},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UO37C3XA}},
  note         = {Machine review of arXiv:2505.01769}
}
abstract

We review the basics of the supersymmetric extension of the Standard Model and discuss the implications of the constraints on the superpartner masses at the LHC for the Higgs mass, the $W$ boson mass, the muon $g-2$ and the proton lifetime.

Figures

Figures reproduced from arXiv: 2505.01769 by the authors.

Figure 1
Figure 1. Limits on gluino and squark masses from ATLAS in the left and right plots, respectively, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Limits on the stop mass vs the neutralino mass at LHC, extracted from Refs. [4] and [5]. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. (Left) Superpartner masses in units of GeV and predictions for ∆ [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Searches from prompt and displaced decays of charged sleptons at LHC in the left and [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: Searches from prompt and displaced decays of neutralinos at LHC in the left and right [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: (Left) Proton lifetime in years as a function of the squark mass, [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

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Forward citations

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Reference graph

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    2024 arXiv

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Reviewed August 16, 2026 · model on record in the stance chip above.