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Anomalous muon magnetic moment, supersymmetry, naturalness, LHC search limits and the landscape

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Howard Baer, Vernon Barger, Hasan Serce

High Energy Physics - Phenomenology · Submitted 15 Apr 2021 · 93 references

Pith's verdict: A competent, honest re-application of the authors' own 2004 NSMH idea to the Fermilab result, with one load-bearing step — the LHC-allowedness of sub-700 GeV sleptons — asserted rather than demonstrated.

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arXiv ID2104.07597 (version 2)
Pith IDD5I6A542, Pith's permanent record of this paper and its review
CitationHasan Serce, Howard Baer, Vernon Barger. "Anomalous muon magnetic moment, supersymmetry, naturalness, LHC search limits and the landscape." arXiv:2104.07597 (2021). https://pith.science/paper/D5I6A542
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The paper

The paper claims

The muon g-2 anomaly can survive inside natural supersymmetry only if the first two generations of scalar particles are much lighter than the third, and the authors exhibit a worked model that does it.

The reading

The Fermilab measurement of the muon's anomalous magnetic moment, combined with the earlier Brookhaven result, leaves a discrepancy of $(25.1±5.9)×10^{-10}$ with the standard prediction, about a $4.2σ$ effect. The paper asks whether weak-scale supersymmetry can supply that missing contribution without violating two other constraints: the observed 125 GeV Higgs mass, which in supersymmetry wants multi-TeV stops, and the LHC's null searches for gluinos, stops and sleptons. The authors argue that within models that are also natural — where the weak scale is not finely tuned, measured by $Δ_{EW} < 30$ — the only surviving option is a normal scalar mass hierarchy (NSMH), in which first and second generation matter scalars sit far below third generation ones. They give a benchmark point with a 2342 GeV gluino, a 1348 GeV light stop and a 298 GeV left smuon that yields $Δa_μ^{SUSY} = 18.6×10^{-10}$ at $Δ_{EW} = 29.9$. They then argue the string landscape pulls first and second generation scalars to 10–50 TeV, predicting a muon anomaly contribution around $5×10^{-13}$ — essentially nothing — so a landscape-selected universe would not produce the observed discrepancy.

What carries the argument

The load-bearing device is the normal scalar mass hierarchy embedded in the three-extra-parameter non-universal Higgs mass model (NUHM3), which allows a common mass $m_0(1,2)$ for first/second generation matter scalars separate from $m_0(3)$ for the third generation. Two further pieces do the work. First, the electroweak naturalness measure $Δ_{EW} = max|terms|/(m_Z^2/2)$ from Eq. 3, computed from the over-forty one-loop corrections to the weak scale, which is what converts 'natural' into a numerical cut at $Δ_{EW} ≲ 30$. Second, the renormalization-group $S$-term, which is zero under scalar mass universality but large here because of the $m_{H_u}^2$–$m_{H_d}^2$ splitting; it pushes the right-slepton above a TeV while leaving the left-sleptons below 300 GeV. The landscape section adds a third device: a power-law statistical draw $f_{SUSY} ∼ m_{soft}^n$ on soft terms, tempered by the anthropic requirement that the pocket-universe weak scale stay within a factor of a few of ours.

Extended reading notes

Core claim

The central claim is a conditional one: if supersymmetry is natural in the electroweak sense, and if the LHC Higgs mass and sparticle search limits are taken at face value, then the muon g-2 anomaly can be explained only by a normal scalar mass hierarchy, where $m_0(1,2) ≪ m_0(3)$. The argument runs through a scan of the NUHM2 and NUHM3 models with $123 < m_h < 127$ GeV and $Δ_{EW} < 30$. In NUHM2, where first/second and third generation scalars share a common mass, the multi-TeV stops needed for the Higgs mass drag the sleptons up with them, and every LHC-allowed point falls well below the measured $Δa_μ$ band. Relaxing the generational degeneracy in NUHM3 lets the stops be heavy while the smuons stay light, and the authors' scan then produces points inside the $2σ$ band that also satisfy $m_{g̃} > 2.25$ TeV and $m_{t̃1} > 1.1$ TeV. The benchmark in Table 1 is offered as an explicit existence proof, with a higgsino-like lightest superpartner at 227 GeV, a chargino at 240 GeV, and a smuon–sneutrino pair near 290 GeV. The authors concede that the point is 'perhaps artificial' in taking the first two generations light and degenerate while the third is far heavier.

Load-bearing premise

The claim that a 298 GeV left smuon and 285 GeV muon sneutrino escape the LHC's roughly 700 GeV slepton bound rests on the assertion that the compressed higgsino-like spectrum and the unusual decay $μ̃_L → χ̃_1^- ν_μ$ make the ATLAS/CMS simplified-model exclusion inapplicable, and no detector-level recast or signal-yield estimate is presented to back it.

Editorial extensions

If this is right

  • If the NSMH picture is correct, the light left smuon and muon sneutrino sit just below the LHC's simplified-model slepton bound, so the next round of slepton searches should either find them or close the last window for a natural supersymmetric explanation of the anomaly.
  • The surviving benchmark has a light top squark at 1348 GeV, inside the projected 3000 fb$^{-1}$ HL-LHC reach of about 1.7 TeV, so the high-luminosity run can test the same region that explains g-2.
  • Because the lightest superpartner is higgsino-like, the relic density from neutralinos alone is only $Ω h^2 = 0.015$, leaving room for axions as a second dark matter component.
  • Within the string landscape the predicted contribution is around $5×10^{-13}$, so a landscape-selected universe would show no muon g-2 anomaly at all; the observed discrepancy would then count against that selection rather than for it.
  • If the lattice evaluation of hadronic vacuum polarization is confirmed, the standard-model prediction moves into agreement with experiment and the entire supersymmetric explanation loses its motivation.

Reading between the lines

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

  • The NSMH spectrum correlates g-2 with lepton-flavor violation: light first and second generation sleptons with non-universal masses generically induce $μ → eγ$ at rates that upcoming experiments can reach, so a null result there would pressure the same corner of parameter space the authors rely on.
  • The benchmark's escape from the slepton bound depends on a 13 GeV chargino–neutralino mass gap that makes the visible decay products soft; a dedicated soft-lepton plus low missing-energy search, rather than a simplified-model reinterpretation, is the natural way to test it.
  • The paper's two escape routes — NSMH survival or a revised hadronic vacuum polarization — are mutually exclusive explanations of the same data, so an independent lattice consensus on the HVP would decide between them without any collider input.
  • The landscape argument turns a cosmological selection principle into a numerical prediction for a precision observable; if soft-term draws were logarithmic rather than power-law, the predicted $Δa_μ$ distribution would shift, making the g-2 prediction a probe of the statistical measure itself.
Original abstract

The recent measurement of the muon anomalous magnetic moment a_\mu\equiv (g-2)_\mu/2 by the Fermilab Muon g-2 experiment sharpens an earlier discrepancy between theory and the BNL E821 experiment. We examine the predicted \Delta a_\mu\equiv a_\mu(exp)-a_\mu(th) in the context of supersymmetry with low electroweak naturalness (restricting to models which give a plausible explanation for the magnitude of the weak scale). A global analysis including LHC Higgs mass and sparticle search limits points to interpretation within the normal scalar mass hierarchy (NSMH) SUSY model wherein first/second generation matter scalars are much lighter than third generation scalars. We present a benchmark model for a viable NSMH point which is natural, obeys LHC Higgs and sparticle mass constraints and explains the muon magnetic anomaly. Aside from NSMH models, then we find the (g-2)_\mu anomaly cannot be explained within the context of natural SUSY, where a variety of data point to decoupled first/second generation scalars. The situation is worse within the string landscape where first/second generation matter scalars are pulled to values in the 10-50 TeV range. An alternative interpretation for SUSY models with decoupled scalar masses is that perhaps the recent lattice evaluation of the hadronic vacuum polarization could be confirmed which leads to a Standard Model theory-experiment agreement in which case there is no anomaly.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,929 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.60 · human participants 0.02 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.68 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The recent measurement of the muon anomalous magnetic moment a_\mu\equiv (g-2)_\mu/2 by the Fermilab Muon g-2 experiment sharpens an earlier discrepancy between theory and the BNL E821 experiment. We examine the predicted \Delta a_\mu\equiv a_\mu(exp)-a_\mu(th) in the context of supersymmetry with low electroweak naturalness (restricting to models which give a plausible explanation for the magnitude of the weak scale). A global analysis including LHC Higgs mass and sparticle search limits points to interpretation within the normal scalar mass hierarchy (NSMH) SUSY model wherein first/second generation matter scalars are much lighter than third generation scalars. We present a benchmark model for a viable NSMH point which is natural, obeys LHC Higgs and sparticle mass constraints and explains the muon magnetic anomaly. Aside from NSMH models, then we find the (g-2)_\mu anomaly cannot be explained within the context of natural SUSY, where a variety of data point to decoupled first/second generation scalars. The situation is worse within the string landscape where first/second generation matter scalars are pulled to values in the 10-50 TeV range. An alternative interpretation for SUSY models with decoupled scalar masses is that perhaps the recent lattice evaluation of the hadronic vacuum polarization could be confirmed which leads to a Standard Model theory-experiment agreement in which case there is no anomaly.

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 The recent measurement of the muon anomalous magnetic moment a_\mu\equiv (g-2)_\mu/2 by the Fermilab Muon g-2 experiment sharpens an earlier discrepancy between theory and the BNL E821 experiment. background 1.00 0.05 0.03 asserted 1.00
s1 We examine the predicted \Delta a_\mu\equiv a_\mu(exp)-a_\mu(th) in the context of supersymmetry with low electroweak naturalness (restricting to models which give a plausible explanation for the magnitude of the weak scale). contribution 0.91 0.72 0.06 asserted 0.59
s2 A global analysis including LHC Higgs mass and sparticle search limits points to interpretation within the normal scalar mass hierarchy (NSMH) SUSY model wherein first/second generation matter scalars are much lighter than third generation scalars. result 0.92 0.83 0.47 asserted 0.79
s3 We present a benchmark model for a viable NSMH point which is natural, obeys LHC Higgs and sparticle mass constraints and explains the muon magnetic anomaly. contribution 0.94 0.92 0.25 asserted 1.00
s4 Aside from NSMH models, then we find the (g-2)_\mu anomaly cannot be explained within the context of natural SUSY, where a variety of data point to decoupled first/second generation scalars. result 0.87 0.90 0.33 asserted 1.00
s5 The situation is worse within the string landscape where first/second generation matter scalars are pulled to values in the 10-50 TeV range. interpretation 0.51 0.47 0.12 asserted 0.98
s6 An alternative interpretation for SUSY models with decoupled scalar masses is that perhaps the recent lattice evaluation of the hadronic vacuum polarization could be confirmed which leads to a Standard Model theory-experiment agreement in which case there is no anomaly. interpretation 0.92 0.27 0.09 hedged possibility 0.76

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from analysis of existing data 0.94.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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. Value of ∆a SUSY µ from natural SUSY vs. naturalness measure ∆EW. Gray dots are from NUHM2,3 models with 123 GeV < mh < 127 GeV but which violate LHC search limits. Orange (NUHM2) and blue (NUHM3) points are LHC-allowed. Green (NUHM3) points are LHC-allowed, natural, have the right Higgs mass and occupy the (g − 2)µ 2σ band. points which fulfill all LHC bounds, the naturalness condition and explain the BNL/Fermilab (g − 2)µ anomaly. In
Figure 2. Value of ∆a SUSY µ from natural SUSY vs. gluino mass mg˜. Gray dots are from NUHM2,3 models with 123 GeV < mh < 127 GeV but which violate LHC search limits. Orange (NUHM2) and blue (NUHM3) points are LHC-allowed. Green (NUHM3) points are LHC-allowed, natural, have mh : 123 − 127 GeV and occupy the (g − 2)µ 2σ band. reduced upper bound on mt˜1 where mt˜1 . 1.7 TeV. This is good news for HL-LHC top-squark searches since their projected reach with 3000 fb−1 is to mt˜1 ∼ 1.7 TeV [84]. In
Figure 3. Value of ∆a SUSY µ from natural SUSY vs. light top-squark mass mt˜1 . Gray dots are from NUHM2,3 models with 123 GeV < mh < 127 GeV but which violate LHC search limits. Orange (NUHM2) and blue (NUHM3) points are LHC-allowed. Green (NUHM3) points are LHC-allowed, natural, have the right Higgs mass and occupy the (g − 2)µ 2σ band. moduli vevs and hence each with varying 4 − d laws of physics. The existence of the landscape is by now widely accepted in the string community and indeed it provides the only plausible solution to the cosmological constant problem via Weinberg’s anthropic…
Figure 4. Value of ∆a SUSY µ from natural SUSY vs. left-smuon mass mµ˜L . Gray dots are from NUHM2,3 models with 123 GeV < mh < 127 GeV but which violate LHC search limits. Orange (NUHM2) and blue (NUHM3) points are LHC-allowed. Green (NUHM3) points are LHC-allowed, natural, have the right Higgs mass and occupy the (g − 2)µ 2σ band. energy EFT is the NUHM3 model. The different soft terms should scan independently of each other [90]. The first/second generation soft terms m0(1, 2) are pulled to very large values ∼ 10 − 50 TeV since they contribute to the weak scale via tiny Yukawa-suppressed…
Figure 5. Distribution of ∆a SUSY µ values from an n = 1 power-law draw for soft terms in the string theory landscape where NUHM3 is the low energy EFT. We require the pocket universe weak scale to lie within the ABDS window with mPU weak < 4mOU weak. where m(slepton) ∼ m(LSP) and/or their branching fractions deviate significantly from the ATLAS/CMS simplified model assumption. Otherwise, for the natural models, it is very hard to explain the anomaly while simultane￾ously requiring the calculated value of mh ∼ 123 − 127 GeV and also obeying LHC constraints that mg˜ > 2.25 TeV, mt˜1 > 1.1 TeV

Figures reproduced from arXiv:2104.07597 by the authors.

References
How the literature uses it

46 arXiv papers cite this in 51 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 · 30 sentences without a confident label

Cites it as support 1 paper
Cites it as background 20 papers

What it cites · 61 sentences without a confident label

Uses the method or tool of 2 papers
  • LHC Higgs mass and sparticle limits, 2. is natural ($Δ_=29.9$) 3. provides sufficient contribution to explain the Fermilab/BNL $(g-2)_μ$ anomaly and 4. is dark matter allowed.[This point is generated using a modifed version of Isajet 7.78 [ref] where a common scale choice $Q^2=m__1m__2$ is used to evaluate the Higgs mass and sparticle self-energies [ref] .

    ISAJET 7.69: A Monte Carlo Event Generator for pp, $\bar pp$, and $e^=e^-$ Reactions · A benchmark SUSY point which can explain $(g-2)_μ$ anomaly · 1.00

  • LHC Higgs mass and sparticle limits, 2. is natural ($Δ_=29.9$) 3. provides sufficient contribution to explain the Fermilab/BNL $(g-2)_μ$ anomaly and 4. is dark matter allowed.[This point is generated using a modifed version of Isajet 7.78 [ref] where a common scale choice $Q^2=m__1m__2$ is used to evaluate the Higgs mass and sparticle self-energies [ref] .

    Precision Corrections in the Minimal Supersymmetric Standard Model · A benchmark SUSY point which can explain $(g-2)_μ$ anomaly · 1.00

Uses data or values from 3 papers
Cites as background 21 papers
  • We will appeal to the string theory landscape [ref] , wherein string flux compactifications [ref] lead to an enormous number of metastable string vacua, say $10^500-10^272,000$, each with different moduli vevs and hence each with varying $4-d$ laws of physics.

    The Anthropic Landscape of String Theory · Expected value of $Δa_μ^$ from the landscape · 0.90

  • We will appeal to the string theory landscape [ref] , wherein string flux compactifications [ref] lead to an enormous number of metastable string vacua, say $10^500-10^272,000$, each with different moduli vevs and hence each with varying $4-d$ laws of physics.

    Flux Compactification · Expected value of $Δa_μ^$ from the landscape · 0.90

  • A number of other papers have recently appeared regarding a SUSY interpretation of the Fermilab/BNL $(g-2)_μ$ anomaly [ref] .

    Heavy Bino and Slepton for Muon g-2 Anomaly · Introduction · 0.99

Discussion

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