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REVIEW 2 major objections 3 minor 43 references

Explanation of electron and muon g-2 anomalies in the MSSM

T0 review · 2 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The MSSM can explain both the muon and electron g-2 anomalies without flavor mixing, provided selectrons and a wino-like chargino are light and smuons are heavier.

desk verdict A real existence proof that the MSSM can explain both g-2 anomalies without flavor violation, but the LHC-compatibility pillar is argued, not recast, and the 'sharp prediction' is really an inversion of the fit. read the letter →

arxiv 1908.03607 v2 pith:NA3HENU7 submitted 2019-08-09 hep-ph

Marcin Badziak , Kazuki Sakurai This is my paper · ORCID
classification hep-ph
keywords muong-2electronMSSMsupersymmetrysleptoncharginocompressedspectraanomalousmagneticmoment
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 Minimal Supersymmetric Standard Model can account for both the positive muon and negative electron anomalous magnetic moment deviations simultaneously, without introducing explicit lepton-flavor violation. The key is arranging the two dominant supersymmetric one-loop contributions, the bino-slepton and chargino-sneutrino loops, to dominate in different lepton sectors and with opposite signs, by taking the product of the bino and wino mass parameters negative. The required spectrum has very light selectrons and a wino-like chargino just above the LEP bound, with smuons considerably heavier, and evades current LHC searches because the spectra are compressed, with mass splittings of only a few GeV. If correct, the two anomalies could be the first sign of low-energy supersymmetry with a characteristic degenerate spectrum rather than evidence for flavor-violating new physics.

What carries the argument

The central objects are the two one-loop MSSM amplitudes, the chargino-sneutrino contribution $a_{\chi^{\pm}_1}^{\chi^{\pm}}$ and the bino-slepton contribution $a_{\chi^{0}_1}^{\chi^{0}}$, given in Eqs. (5) and (6). The sign of the chargino-sneutrino term is controlled by $\mathrm{sign}(\mu M_2)$, while that of the bino-slepton term is controlled by $\mathrm{sign}(\mu M_1)$; the paper exploits $M_1 M_2 < 0$ to make the two contributions opposite in sign. The second crucial ingredient is the different decoupling behavior: the bino-slepton contribution falls roughly as $1/m_{\tilde{\ell}}^4$, while the chargino-sneutrino contribution falls more slowly (roughly $1/m_{\tilde{\nu}}^2$ or $1/(\mu M_2)$ in the relevant limits), so raising the smuon masses suppresses the negative bino-smuon term while leaving the positive chargino-sneutrino term to dominate the muon g-2. The selectron left-right mixing term $m_e(\mu\tan\beta - A_e)$ enhances the bino-selectron contribution, making a large negative electron g-2 possible with light selectrons.

What would settle it

A public recast of the ATLAS soft-lepton search (ATLAS-CONF-2019-014) applied to the exact BP-1 and BP-2 production cross-sections and decay kinematics would settle the central claim: if the recast excludes a wino-like chargino near 180 GeV (BP-1) or 120 GeV (BP-2) with splittings of 2-4 GeV, then the claimed evasion fails and the simultaneous explanation collapses.

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Extended reading notes

Core claim

The discovery claim is that both g-2 anomalies can be fitted in the MSSM by choosing the sign relation $M_1 M_2 < 0$ while making the selectron sector light and the smuons heavier. With $\mu M_1 < 0$ the bino-selectron loop gives a negative contribution to the electron g-2, while with $\mu M_2 > 0$ the chargino-sneutrino loop gives a positive contribution to the muon g-2; if smuons are heavy enough the wrong-sign bino-smuon term is suppressed. The paper presents two viable spectra: one with a heavy right-handed smuon (BP-1), and one motivated by Higgs-mediated supersymmetry breaking with both left- and right-handed smuons heavy (BP-2). In both benchmark points the supersymmetric contributions place electron and muon g-2 within $1\sigma$ of the measured central values, with light selectrons and a wino-like chargino of masses about 120-200 GeV that evade LHC constraints because the mass splittings to the bino LSP are only a few GeV and the decay chains are three-body, soft-lepton, or electron-dominated.

Load-bearing premise

The benchmark spectra escape LHC constraints only if the existing compressed-spectrum searches genuinely miss the particular kinematics here, namely mass splittings of only 2-4 GeV, three-body decay chains, and electron-only or very soft final states; a full recast of those searches placing a stronger limit on the wino-like chargino or selectron masses would exclude the claimed parameter space.

Editorial extensions

If this is right

  • A simultaneous fit requires $M_1 M_2 < 0$, so the bino and wino soft masses must have opposite signs; this is a sharp, testable prediction of the MSSM parameter space.
  • Selectrons and the wino-like chargino must be below about 200 GeV (BP-1) or 150 GeV (BP-2), near the LEP bound, with smuons at least several times heavier.
  • The spectra are highly compressed: the wino-like chargino and the bino LSP are split by only 2-4 GeV and sleptons are split by 25-30 GeV, so the model predicts soft-lepton and soft-photon signatures that future dedicated compressed-spectrum searches could observe.
  • Large $\tan\beta$ (at least 15-40 depending on the scenario) and a higgsino mass of order 1 TeV are preferred, while $A$-terms are taken to vanish.
  • No explicit lepton-flavor violation is introduced; in the Higgs-mediated scenario the smuon-selectron mass splitting arises from Yukawa-proportional soft terms, which naturally suppresses $\mu\to e\gamma$.

Reading between the lines

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

  • If the mechanism is correct, a future high-luminosity soft-lepton search at the LHC, or a dedicated search for compressed chargino production, should see an excess in exactly the mass-splitting and final-state configurations described for BP-1 and BP-2.
  • The same sign-splitting trick could generalize beyond the MSSM: any new-physics model with two one-loop contributions whose signs depend on different mass parameters and which decouple at different rates can accommodate opposite-sign lepton g-2 anomalies without flavor violation.
  • The preferred large $\tan\beta$ and light selectron sector may be in tension with other observables such as the Higgs mass and $B$-physics constraints; a full MSSM scan including the Higgs sector could shrink or exclude the benchmark regions.
  • Even without explicit flavor mixing, the large smuon-selectron mass splitting could induce flavor-violating processes at loop level; computing $\mu\to e\gamma$ with the actual spectrum would provide a direct cross-check of the scenario against the MEG bound.
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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 / 3 minor

Summary. The paper proposes a Minimal Supersymmetric Standard Model (MSSM) explanation of the simultaneous deviations in the electron and muon anomalous magnetic moments without introducing explicit lepton-flavour mixing. The key idea is to arrange the two dominant one-loop supersymmetric contributions, the bino-slepton term and the chargino-sneutrino term, so that they have opposite relative signs between the electron and muon sectors. The authors choose M1 and M2 with opposite signs, make smuons heavier than selectrons, and present two benchmark scenarios: BP-1 with a very heavy right-handed smuon, and BP-2 motivated by the Higgs-mediation mass pattern of Eq. (14). Both scenarios require very light selectrons and a wino-like chargino near the LEP bound, with compressed spectra argued to evade LHC searches. The SUSY contributions are computed at one loop following Martin and Wells and cross-checked with MicrOMEGAs; masses, branching ratios, and NLO cross sections are obtained with SuSpect, SDecay, and Prospino. The paper concludes that both g-2 anomalies can be explained within 1 sigma while remaining consistent with LHC constraints.

Significance. If the result holds, the paper provides an existence proof for a lepton-flavour-conserving MSSM parameter region that accommodates the observed electron and muon g-2 anomalies, with two different theoretically motivated mass patterns that achieve the required sign flip. The strengths are that the benchmark points are fully specified, the one-loop calculation is cross-checked against an independent code, and the relevant masses, branching ratios, and NLO cross sections are computed with standard public tools. The main weakness is the LHC-constraint analysis: the paper argues qualitatively that compressed spectra and particular decay kinematics make existing searches inapplicable, but it does not perform a recast or a quantitative acceptance estimate. Since LHC consistency is a central part of the claim, the significance is conditional on a more rigorous collider treatment.

major comments (2)
  1. [Sec. 3.1] The claim that BP-1 evades LHC constraints is under-supported. The paper notes that ATLAS-CONF-2019-014 quotes a lower limit near 170 GeV for a chargino with a 4 GeV mass splitting in the chi_1^+- chi_2^0 -> W* Z* chi_1^0 chi_1^0 simplified topology, and that BP-1 has m(chi_1^+-) about 179.7 GeV. However, the argument that this limit cannot be applied because BP-1 has chi_1^+ chi_1^- production and three-body decays requires quantitative verification via a recast: the ATLAS limit comes from a shape fit, and a different production and decay chain can have a different acceptance. With sigma(chi_1^+- chi_2^0) about 2.44 pb and sigma(chi_1^+ chi_1^-) about 1.21 pb, the signal is not negligible, and no estimate of the passing event rate is given. Without such an estimate, the conclusion that BP-1 is allowed by the LHC is not established.
  2. [Sec. 4.1] The LHC-consistency argument for BP-2 is similarly qualitative and more delicate because the masses are closer to the quoted limits. The wino-like chargino has mass 123.5 GeV with a 2 GeV splitting, and the paper quotes the ATLAS soft-dilepton limit as about 100 GeV for that splitting. The production cross sections are large: sigma(chi_1^+- chi_2^0) about 8.89 pb and sigma(chi_1^+ chi_1^-) about 4.48 pb. The paper argues that electron-only final states and mostly invisible neutralino decays make the searches inapplicable, but no recast or acceptance estimate is provided. The smuon discussion compares the total dimuon cross section (about 0.14 fb) with a cross-section limit (about 0.24 fb) without including selection efficiencies, which is not a rigorous exclusion. A full or simplified recast of the relevant soft-lepton and slepton searches is needed before BP-2 can be claimed to satisfy the LHC constraints.
minor comments (3)
  1. [Sec. 2, text after Eq. (10)] The decoupling limits in the text have the wrong signs: with the definitions in Eqs. (1), (2), and (10), the no-SUSY limits are R_SUSY_mu approx -3.8 and R_SUSY_e approx +2.4, not the values '3.8' and '-2.4' as printed. The benchmark-point values and Figure 1 are consistent with the correct signs, so this appears to be an exposition error.
  2. [Figure 3] The caption indicates a scan in the tan beta-mu plane, but the label inside the plot still reads 'tan beta = 60', which is inconsistent with the scanned variable and should be corrected.
  3. [Sec. 3.1] The sentence 'The BP-1 evades this constraints' contains a grammatical error and should be rephrased.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MSSM parameter choices are fitted to the g-2 data, and the paper explicitly labels the resulting spectrum as a fit, not an independent prediction.

full rationale

The paper's derivation chain is a standard MSSM parameter scan rather than a derivation of the anomalies from first principles. The benchmark points BP-1 and BP-2 explicitly list soft parameters, and the SUSY contributions a_e^SUSY and a_mu^SUSY are computed with the established one-loop formulas (Eqs. 5 and 6) and independently cross-checked with MicrOmegas. The paper does not claim to predict Delta-a_e and Delta-a_mu from unconstrained inputs; it states that the parameters are fitted to the measured anomalies, e.g., 'Fitting simultaneously (g-2)_e and (g-2)_mu leads to quite sharp prediction for the electroweak part of the MSSM spectrum.' The word 'prediction' there refers to the inferred sparticle spectrum, which is a consequence of the fit, but the central existence claim—that the MSSM can accommodate both anomalies without flavour mixing—is established by explicit computation against external experimental constraints (LEP, LHC searches). The self-citations (e.g., Ref. [31] for bino-wino mixing suppression) are peripheral remarks on mass splitting and are not load-bearing for the central result. The LHC-evasion arguments are kinematic and not based on a full recast, but that is a robustness or correctness concern, not circularity. No step in the chain is equivalent by construction to its input.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a large number of tunable MSSM parameters that are adjusted to fit the two g-2 anomalies. The only axioms are the MSSM itself, the standard one-loop formulas, the interpretation of the anomalies as signals, and, in the second scenario, the Higgs-mediation ansatz. The LHC-evasion assumption is load-bearing for the existence proof.

free parameters (8)
  • M1 (bino soft mass) = -180 GeV (BP-1), -125 GeV (BP-2)
    Chosen with sign opposite to M2 so the bino-selectron loop gives a negative contribution to the electron; magnitude tuned to fit Δae.
  • M2 (wino soft mass) = 170 GeV (BP-1), 118 GeV (BP-2)
    Sets the wino-like chargino mass near the LEP bound and makes the chargino-sneutrino contribution positive for the muon.
  • μ (higgsino mass parameter) = 1700 GeV (BP-1), 700 GeV (BP-2)
    Large μ enhances the μ tanβ term in the bino-selectron mixing; the value is tuned to fit both anomalies and to control the chargino contribution.
  • tanβ = 60 (both benchmarks); lower bound varies with scenario (about 15 for BP-1-like, about 40 for BP-2-like)
    Enhances both SUSY contributions roughly linearly; set to the large value needed to reach the measured magnitudes.
  • m_tilde_E1 (right-handed selectron soft mass) = 200 GeV (BP-1), 120 GeV (BP-2)
    Light selectron is required to make the bino-selectron loop large enough to explain the electron anomaly.
  • m_tilde_L1 = m_tilde_L2 (left-handed slepton soft masses) = 200 GeV (BP-1), 140 GeV (BP-2)
    Left-handed sleptons are also light so the chargino-sneutrino loop remains sizable for the muon.
  • m_tilde_E2 (right-handed smuon soft mass) = 2000 GeV (BP-1); 711.6 GeV physical mass in BP-2 (from m_H = 700 GeV)
    A heavy right-handed smuon suppresses the wrong-sign bino-smuon loop so the chargino contribution dominates for the muon.
  • m_H (Higgs-mediation mass parameter) = 700 GeV (BP-2); not used in BP-1
    In the second scenario, m_H sets the splitting between electron and muon sleptons via the Higgs-mediation ansatz.
assumptions (5)
  • domain assumption The MSSM is the underlying framework with its standard particle content and interactions.
    The entire analysis is performed within the Minimal Supersymmetric Standard Model; no beyond-MSSM states are introduced.
  • standard math The one-loop SUSY contributions are given by Eqs. (5) to (8), taken from Moroi and Martin and Wells.
    These published formulas are the accepted state-of-the-art one-loop expressions; the paper does not re-derive them.
  • domain assumption The measured deviations Δae and Δaμ in Eqs. (1) and (2) represent genuine new physics signals.
    The paper takes the SM predictions and the 2018 fine-structure constant measurement at face value and does not discuss SM theory uncertainties.
  • domain assumption In the second scenario, the soft mass matrices have the Higgs-mediation form of Eqs. (14) and (15).
    This ansatz, borrowed from refs. [38,39], is what naturally aligns the slepton mass matrices and suppresses μ→eγ in the Higgs-mediation scenario.
  • domain assumption Existing LHC compressed-spectrum searches do not exclude the benchmark points.
    The paper infers this from qualitative kinematic arguments (2-4 GeV splittings, three-body decays, electron-only final states) rather than from a full recast.

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Cite this review

Pith. "Pith review of Explanation of electron and muon g-2 anomalies in the MSSM." pith.science (2026). https://pith.science/paper/NA3HENU7

@misc{pith2026190803607,
  author       = {Pith},
  title        = {Pith review of: Explanation of electron and muon g-2 anomalies in the MSSM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NA3HENU7}},
  note         = {Machine review of arXiv:1908.03607}
}
read the original abstract

The current experimental values of anomalous magnetic moments of muon and electron deviate from the Standard Model predictions by few standard deviations, which might be a hint of new physics. The sizes and signs of these deviations are different and opposite between the electron and muon, which makes it difficult to explain both of these anomalies in a consistent model without introducing large flavour-violating effects. It is shown that they can be simultaneously explained in the Minimal Supersymmetric Standard Model (MSSM) by arranging the sizes of bino-slepton and chargino-sneutrino contributions differently between the electron and muon sectors. The MSSM spectrum features very light selectrons and wino-like chargino, while they can evade LHC constraints due to degenerate spectra.

Figures

Figures reproduced from arXiv: 1908.03607 by the authors.

Figure 1
Figure 1. RSUSY l (solid), R χ± l (dashed) and R χ 0 l (dashed-dotted) for electron (red) and muon (blue) as a function of mµ˜R . Very thin dotted lines around 1 (red for electron) and -2 (blue for muon) correspond to −∆al/(2σl), which R χ± l and R χ 0 l approach in the decoupling limit. show the effect of the bino-slepton and chargino-sneutrino contributions, we introduce R χ±/χ0 l = 2a χ±/χ0 l − ∆al 2σl , (9) such that R SU… view at source ↗
Figure 2
Figure 2. Contours of SUSY contribution to electron (yellow) and muon (blue) g − 2 in the plane of µ and M2 = mE˜1 = mL˜1 = mL˜2 for tan β = 60 and M1 = −(M2 − 20 GeV). In the left (right) plot mµ˜R is 5 (20) times larger than M2 and the other sleptons. has a wrong sign. This is because in this region the bino contribution dominates a SUSY µ , which is proportional to M1µ < 0. When increasing the mµeR the absolute value of th… view at source ↗
Figure 3
Figure 3. The same as in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The same as in fig. 1 but as a function of mH in the scenario motivated by the Higgs mediation of SUSY breaking. Values of the relevant SUSY parameters are given above the plot. where mχ˜ ± 2 = max(|µ|, |M2|). We see that in this case the chargino-sneutrino contributio…
Figure 5
Figure 5. Figure 5: Left panel: The same as in fig. 2 but in the scenario motivated by the Higgs mediated SUSY breaking with mH = 700 GeV. Right panel: The same as in fig. 3 but in the µ–mH plane. selectrons. From the left panel of fig. 5 we see that for mH = 700 GeV, the selectron and wi…

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