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REVIEW 4 major objections 5 minor 63 references

Analytical Soft SUSY Spectrum in Supersymmetric Models in Light of $ S_{4} \times Z_{n} $ flavor symmetric SUSY SO(10) theory

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In the $S_4 \times Z_n$ type-II seesaw SO(10) framework, the $\mu \to e \gamma$ rate is computed to sharply separate CMSSM, NUHM, and NUSM supersymmetry-breaking patterns, with MEG-II projected to probe nearly all of NUHM and much of NUSM…

desk verdict A useful but under-verified parameter scan: the qualitative CMSSM/NUHM/NUSM hierarchy under MEG-II is credible, but the paper's own leading-log caveat and an unphysical table entry keep the quantitative boundaries from being trusted. read the letter →

arxiv 1908.11160 v2 pith:TWUL2NDN submitted 2019-08-29 hep-ph

Gayatri Ghosh This is my paper · ORCID
classification hep-ph
keywords leptonflavorviolationmutoegammasupersymmetrySO(10)grandunifiedtheoryS4symmetrytype-IIseesawnon-universalHiggsmodelMEGexperiment
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 in a supersymmetric SO(10) grand unified theory with an $S_4 \times Z_n$ flavor symmetry and a type-II seesaw for neutrino masses, the decay $\mu \to e \gamma$ becomes a sharp discriminator among three supersymmetry-breaking patterns. It claims that the current MEG upper bound $\text{BR}(\mu\to e\gamma) < 4.2 \times 10^{-13}$ and the projected MEG-II sensitivity of $6 \times 10^{-14}$ leave almost disjoint surviving regions: CMSSM must have very heavy scalar and gaugino masses, NUHM can be light only because of cancellations in the off-diagonal slepton-mass entries, and NUSM allows a wide range of masses. If these predictions are right, the next round of muon lepton-flavor-violation experiments would effectively survey the NUHM and NUSM parameter spaces while leaving CMSSM mostly untouched, offering a way to distinguish the models at the HE/HL-LHC.

What carries the argument

The central machinery is the leading-log mass-insertion approximation for the off-diagonal left-handed slepton mass matrix. In the $S_4\times Z_n$ type-II seesaw SO(10) model, the Dirac neutrino Yukawa matrix $f_\nu$ is fixed by the flavor symmetry, and the entries $(\delta_{LL})_{ij}$ are proportional to $(f_\nu^\dagger)_{ik}(f_\nu)_{jk}\log(M_X/M_{R_k})$. For CMSSM the prefactor is $(-3m_0^2 + A_0^2)/(8\pi^2)$, while for NUHM it becomes $(-2m_0^2 + A_0^2 + m_{H_u}^2)/(8\pi^2)$, and the relative sign between $m_{H_u}^2$ and $m_0^2$ is what permits cancellations. The numerical scans use the paper's chosen spectrum and LFV computation code, with full two-loop RGE running of the Yukawa couplings.

What would settle it

Compute $\text{BR}(\mu\to e\gamma)$ by full two-loop RGE running of the $S_4\times Z_n$ Dirac neutrino Yukawa matrix at representative points (for instance $m_0 = 8$ TeV, $M_{1/2} = 3$ TeV, $\tan\beta = 5$) and compare with the leading-log formula; an order-of-magnitude discrepancy would shift the claimed allowed regions. Alternatively, a null result from MEG-II would exclude every predicted NUHM point whose central rate exceeds $6\times 10^{-14}$, directly contradicting the paper's claim that almost all of NUHM lies within MEG-II reach.

Watch

Extended reading notes

Core claim

Using the $S_4 \times Z_n$ constrained type-II seesaw framework, the paper computes the lepton-flavor-violating mass insertions $(\delta_{LL})_{ij}$ from the Dirac neutrino Yukawa couplings at the GUT scale and evaluates $\text{BR}(\mu\to e\gamma)$ under CMSSM, NUHM, and NUSM boundary conditions. The central finding is that the current bound of $4.2\times 10^{-13}$ and the future reach of $6\times 10^{-14}$ carve out qualitatively different allowed regions: CMSSM requires $m_0$ roughly 4.5--8 TeV with $M_{1/2}$ above about 3 TeV and a narrow $\tan\beta$ band; NUHM permits spectra as light as about 1 TeV in $M_{1/2}$ because negative $A_0$ and the Higgs soft mass $m_{H_u}$ partially cancel against $m_0^2$ in the off-diagonal slepton mass; and NUSM with multi-TeV first-two-generation scalars survives over $M_{1/2}$ from about 1 to 6 TeV and $m_0$ up to 16 TeV, with $\tan\beta$ restricted to 5--47 and, for $m_h \simeq 125.9$ GeV, to 15--30. The paper reads these differing fates as a way to distinguish the three supersymmetry-breaking patterns at MEG-II and the HE/HL-LHC.

Load-bearing premise

The load-bearing premise is that the leading-log mass-insertion formulas with the tabulated $\delta$ values give the right branching fractions, even though the paper concedes that for $M_{1/2}$ around 1 TeV the result may differ from a full RGE evaluation by up to a factor of 10.

Editorial extensions

If this is right

  • MEG-II at $6\times 10^{-14}$ would probe essentially all of the NUHM parameter space that survives the 2016 MEG bound, because the cancellation mechanism keeps rates above the future sensitivity.
  • In CMSSM, only very heavy spectra ($m_0 \sim 4.5$--$8$ TeV, $M_{1/2} \gtrsim 3$ TeV) remain, so a null MEG-II result would not further constrain CMSSM, while a positive signal would strongly disfavor it.
  • In NUSM, MEG-II would restrict $\tan\beta$ to below about 20, and the surviving points predict low LFV rates, making MEG-II and HE/HL-LHC complementary probes.
  • The model-by-model allowed regions listed in the summary tables provide direct target lists for HE/HL-LHC sparticle searches, since each model corresponds to a distinct $m_0$--$M_{1/2}$--$A_0$ pattern.

Reading between the lines

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

  • If the paper's admitted factor-of-10 uncertainty in the leading-log formula propagates up to $M_{1/2}$ of several TeV, the true exclusion boundaries could shift by thousands of GeV; a dedicated full-RGE benchmark scan on the $S_4\times Z_n$ $f_\nu$ matrix would settle this.
  • Because the $S_4\times Z_n$ model fixes the relative sizes of $\delta_{12}$, $\delta_{23}$, and $\delta_{31}$, a future measurement of $\tau\to\mu\gamma$ and $\tau\to e\gamma$ alongside $\mu\to e\gamma$ would test the flavor-symmetry structure itself, not just the individual rates.
  • The paper does not derive the tabulated $\delta$ values from the model's vacuum alignments; deriving them would turn the phenomenological scan into a first-principles test of the flavor symmetry, and any inconsistency would point to corrections to the leading-log or type-II seesaw assumptions.
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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

4 major / 5 minor

Summary. This paper studies the charged-lepton-flavor-violating decay mu -> e gamma in supersymmetric SO(10) models with an S4 x Z_n flavor symmetry and type-II seesaw neutrino masses. Using the Dirac neutrino Yukawa texture of Ref. [28], the author scans the soft SUSY-breaking parameter space of CMSSM, NUHM, and NUSM with the public code SuSeFLAV and applies the MEG 2016 bound BR(mu -> e gamma) < 4.2 x 10^-13 and the projected MEG-II sensitivity 6 x 10^-14. The main results are allowed regions in (m0, M1/2, tan beta, A0) for each model: CMSSM survives only for heavy spectra, NUHM allows much lighter spectra because of cancellations involving m_Hu, and NUSM leaves a wide range of M1/2 up to about 6 TeV. The paper also comments on the reach of HE/HL-LHC for the surviving spectra.

Significance. If the numerical results were fully supported, the paper would provide a useful model-discrimination statement for MEG-II and HL-LHC: the three SUSY boundary conditions produce qualitatively different allowed regions, and the projected MEG-II sensitivity would probe essentially all of NUHM and much of NUSM while leaving CMSSM largely untouched. The use of the public SuSeFLAV package and of an externally published S4 x Z_n Yukawa texture are appropriate, and the comparison with the current MEG limit is concrete. However, the quantitative boundaries are not currently reproducible from the text: the key delta_ij inputs are not derived, one table entry is unphysical, and the relationship between the leading-log equations and the claimed full two-loop running is not resolved. The qualitative hierarchy is plausible and consistent with the earlier literature, but the specific mass limits should be treated with caution until the inputs are documented.

major comments (4)
  1. [Sec. III, Table I and Eqs. (5)-(7)] The numerical inputs that drive the LFV predictions are stated without derivation: the Dirac neutrino Yukawa matrix f_nu from [28] is not displayed, not even the (1,3), (2,3), and (3,3) combinations that enter Eqs. (5)-(7), and no intermediate calculation is shown that yields delta_12 = 0.6672 x 10^-4, delta_23 = 1.5634 x 10^-4, or delta_31 = 0.7377 x 10^43. The last value is impossible as a dimensionless mass insertion and indicates at least a typographical error. Because delta_ij is defined in Sec. II.A as Delta_ij / m_tilde_l^2, fixed table values also presuppose a fixed slepton scale that is not specified. Please provide f_nu or a step-by-step derivation, correct the table, and state how the table entries are used in the SuSeFLAV runs. This is load-bearing because the excluded/allowed boundaries in Figs. 3-8 ultimately rest on these numbers.
  2. [Sec. II.A (after Eq. (13)) and Sec. IV] The paper's own caveat after Eq. (13) states that for M1/2 around 1 TeV the branching fractions can differ by up to a factor of 10 from the full RGE running, while the abstract and Sec. IV claim that the numerical analysis includes full two-loop RGE running. Since the scans extend to M1/2 of 4.5-6 TeV and the NUSM lower boundary sits at M1/2 around 1 TeV, which is exactly where the stated factor-of-10 discrepancy applies, the text must state explicitly which figures are produced by SuSeFLAV's full running and which by the leading-log equations (3) and (13). Without this specification, a factor-of-10 uncertainty applies to the lower boundaries and the sharp quantitative limits quoted in Sec. IV are not supported as stated.
  3. [Sec. IV and Tables II-III] Several central quantitative statements are read from scatter plots without documented acceptance or rejection criteria or scan density; examples include Sec. IV.A's statement that m0 lies between 4.5 TeV and 8 TeV and the ranges compiled in Tables II and III. In addition, the column headers of Tables II and III are inconsistent, with Table III's first column labeled 'CMSSM' although the section and table title concern NUSM. Please provide the SuSeFLAV input files or benchmark points, and state the number of scan points and the criterion for 'allowed'. Without this, the printed boundaries are not reproducible and the reader cannot tell whether they reflect the S4 x Z_n texture or internal choices of the scan.
  4. [Abstract and Sec. IV] The abstract states that regions excluded by LHC searches are specified, but the results sections apply only the MEG bound, the Higgs-mass window, and projected sensitivities; no explicit LHC sparticle-search exclusion, such as gluino or squark mass limits, is referenced or overlaid in the figures. Either add the LHC constraints actually used, or soften the claim in the abstract and conclusion to match what is presented.
minor comments (5)
  1. [Title and Abstract] The title contains a typo, 'L ight' for 'Light', and the abstract has 'for the the above mentioned'; these should be corrected.
  2. [Throughout] There are repeated language and typographical errors, including 'Feynmann' for 'Feynman', 'paramater' for 'parameter', and inconsistent formatting such as 'SuSeFL A V'; a careful editorial pass is needed.
  3. [Sec. IV.A] The sentence 'the parameter space M1/2 >= 10 GeV is permitted by present MEG bounds' is clearly missing a factor of 10^3 and should read at least 1 TeV, consistent with the surrounding discussion and Table II.
  4. [Sec. II.B] After Eq. (9), the neutrino masses are listed as 'm_nu3 = 0.05 eV, m_nu3 = 0.01 eV, and m_nu1 = 0.005 eV'; the second occurrence of m_nu3 should be m_nu2.
  5. [References] References [29] and [39] appear to be the same paper and are redundant; please check and consolidate them.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction: the LFV rates are a scan of SUSY soft parameters using the external S4×Zn Yukawa texture [28] and external MEG bounds; the only self-citation ([31]) is contextual, not load-bearing.

full rationale

The paper's derivation chain is: (i) take the S4×Zn Dirac neutrino Yukawa matrix from [28] (Dutta et al., not the present author); (ii) use standard leading-log mass-insertion formulas, eqs. (3), (5)–(7), with the δij values in Table I stated as computed from that fν; (iii) feed these into the public code SuSeFLAV [50] while scanning the soft parameters of CMSSM, NUHM, and NUSM; (iv) compare the resulting BR(μ→eγ) with the MEG 2016 upper limit and the projected MEG-II sensitivity. No parameter is fitted to the MEG data: the δij are fixed model inputs and the MEG bound is an external constraint, so the exclusion contours are not forced by construction. The central qualitative result—CMSSM needs heavier spectra while NUHM can be lighter due to cancellations and NUSM admits a wide region—follows from the scan and the soft-mass dependence of the LFV amplitude, not from any definitional equivalence. The only self-citation, [31] (Bora–Ghosh), is used for the NUSM parameterization and for the A0=0 leading-log expression, but the NUSM setup is also attributed to [39] (Bhattacharya et al.) and the mass-insertion formulas are standard (cf. [51]), so this self-citation is not load-bearing. The apparent Table I entry δ31 = 0.7377×10^43 is unphysical as rendered, and the intermediate calculation of the δij from fν is not shown, but these are transparency/reproducibility issues rather than circularity; moreover, the μ→eγ channel of interest depends on δ12 through eq. (5), not δ31. The paper's own caveat after eq. (13)—that at M1/2 ~ 1 TeV the leading-log branching fraction can differ by up to a factor of 10 from full RGE running—is a numerical-accuracy limitation, not a circular step. Overall, there is no significant circularity; the score of 2 reflects only the minor, non-load-bearing self-citation to [31].

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

The paper imports the S4 x Zn flavor structure and f_nu from earlier work, assumes type-II seesaw, and uses leading-log plus SuSeFLAV numerics; the Table 1 delta values are not derived in the text. The central claim therefore rests on external model results and an approximation whose own stated breakdown range overlaps the scan range.

free parameters (7)
  • m0 (universal scalar mass) = 0-8 TeV (CMSSM), 30 GeV-8 TeV (NUHM), 0-16 TeV (NUSM)
    Scanned over the stated ranges; no fit to LFV data.
  • M1/2 (universal gaugino mass) = 0.3-4.5 TeV (CMSSM), 30 GeV-5 TeV (NUHM), 0-6 TeV (NUSM)
    Scanned over the stated ranges.
  • A0 (universal trilinear coupling) = -3m0 to +3m0 (CMSSM), -24 to +24 TeV (NUHM), 0 (NUSM)
    Scanned; central to Higgs-mass and LFV dependence.
  • tan beta = 1-60
    Scanned; important for LFV rates and Higgs mass.
  • mHu and mHd (NUHM Higgs soft masses) = -9.5 to +9.5 TeV
    Only in NUHM; cancellation between mHu and m0 drives the lighter allowed spectra.
  • RH neutrino masses MR1, MR2, MR3 = 1e13 GeV, 1e14 GeV, 1e16 GeV
    Chosen in Section III; they enter the leading-log factors.
  • delta12, delta23, delta31 (mass insertions from Table 1) = 0.6672e-4, 1.5634e-4, 0.7377e43 (as printed)
    Listed as inputs to eqs. (5)-(7) but their derivation from f_nu is not shown; delta31 as printed is an obvious typo.
assumptions (5)
  • domain assumption The Dirac neutrino Yukawa matrix f_nu from the S4 x Zn model [28] is correct and applicable at the GUT scale.
    Eq. (4) defines f_nu from M_D, but the numerical matrix is not given in this paper; all LFV predictions inherit it from [28].
  • domain assumption The leading-log mass-insertion approximation (eqs. (3),(5)-(7),(13)) accurately captures the LFV rates over the scanned parameter space.
    The paper's own caveat (Section IV.B) says BR can differ by a factor of 10 for M1/2 about 1 TeV, while the scans reach 5-6 TeV.
  • domain assumption The neutrino mass matrix in eq. (8) arises from a type-II seesaw mechanism within the S4 x Zn SO(10) model.
    The relation between M_nu and f_nu is assumed, not derived in this paper.
  • domain assumption SuSeFLAV correctly implements the 2-loop RGEs and the LFV computation.
    All numerical results come from the public package [50]; no independent validation is given.
  • domain assumption The SUSY breaking boundary conditions for CMSSM, NUHM and NUSM are as stated.
    The scans are defined by these scenarios in Section III.

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Cite this review

Pith. "Pith review of Analytical Soft SUSY Spectrum in Supersymmetric Models in Light of $ S_{4} \times Z_{n} $ flavor symmetric SUSY SO(10) theory." pith.science (2026). https://pith.science/paper/TWUL2NDN

@misc{pith2026190811160,
  author       = {Pith},
  title        = {Pith review of: Analytical Soft SUSY Spectrum in Supersymmetric Models in Light of $ S_4 \times Z_n $ flavor symmetric SUSY SO(10) theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TWUL2NDN}},
  note         = {Machine review of arXiv:1908.11160}
}
abstract

The heavy right-handed neutrinos in supersymmetric models can act as the source of lepton flavor violation (LFV). LFV processes like $ \mu \rightarrow e \gamma $, $ \tau \rightarrow \mu \gamma $, $ \tau \rightarrow e \gamma $ is an effective way to explore new physics beyond the SM. Among the possible processes, $ \mu $ decays have the greatest discovery potential in most of the supersymmetric models. Experimental inference of lepton flavor-violating processes within a supersymmetric type-II seesaw framework in the non-universal Higgs model (NUHM) and non-universal Scalar Mass model for Yukawa mixing scenarios in the $ S_{4} $ theory with an additional discrete symmetry is presented. The numerical analysis includes full 2 loop renormalization group running effects for the the above mentioned Yukawa coupling matrices. The projected discovery reach of LFV experiments (MEG-II) is mentioned and those regions in mSUGRA, NUHM, NUSM models that have already been excluded by the LHC searches or that which is probed by MEG experiments is specified here. The results presented in this work can influence experimental challenges and physics motivations to construct various BSM theories and sensitivity to test these theories at next run of HE/HL LHC is also considered.

Figures

Figures reproduced from arXiv: 1908.11160 by the authors.

Figure 1
Figure 1. Examples of Feynmann Diagrams contributing to τ → µ + γ processes in SUSY models. The SUSY SO(10) theory obviously embraces the seesaw mechanism. The existence of heavy RH neutrinos at an intervening scale give on to the running and originate flavor violating entries in the left-handed slepton mass matrix at the weak scale [11]. The lepton flavour violating entries in the SO(10) SUSY GUT framework can be percieved i… view at source ↗
Figure 2
Figure 2. Examples of Feynmann Diagrams contributing to µ → e + γ processes in SUSY models. where MSUSY is mas scale of the SUSY particles, α is the fine structure constant and GF is the Fermi constant. The 6 × 6 slepton mass matrix is described as m2 ¯(L) =   m2 ¯(L) )(LL)ij m2 ¯(L) )(LR)ij m2 ¯(L) )(RL)ij m2 ¯(L) )(RR)ij   (2) where LL, RL, LR, RR are 3× 3 entries established on the chirality tag of sfer… view at source ↗
Figure 3
Figure 3. The outcome of the calculations are presented for CMSSM case. In fig 3a, 3b, different horizontal lines depicts the present (MEG 2016) and future MEG constraints for BR(µ → e + γ). B. Non Universal Higgs Model (NUHM) The cMSSM+RHN model parameter set is investigated in the literature [54–56]. Also, the NUHM1 +RHN models were extensively studied for specific non-universal scenarios with the following GUT-scale mass r… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: In figs (4a-4e) allowed SUSY parameters region as constrained by MEG 2016 bound is presented [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: The consequences of the analysis and calculations are presented for NUHM case. In fig 5a,5b, different horizontal lines illustrates the present (MEG 2016) by MEG Collaboration and future MEG bounds for BR(µ → e + γ). Figs. 5c,5d portrays the allowed SUSY parameter spac…
Figure 6
Figure 6. Figure 6: Figs. 6a-6d describe the allowed SUSY region for different soft SUSY parameter space, as is obstructed by stringent MEG 2016 bounds. MGUT is presented. In fig.7a, the soft SUSY parameter space as allowed by present and future MEG bounds on BR(µ → eγ) is depicted. For t…
Figure 7
Figure 7. Figure 7: The results of the analysis are presented for NUSM case. In fig 7a, 7b, different horizontal lines depicts the present (MEG 2016) and future MEG bounds for BR(µ → e + γ). Figs. 7c, 7d shows the allowed space for different parameters, that is allowed by MEG 2016 bound. …
Figure 8
Figure 8. Figure 8: The results of the computations presented for NUSM case. Fig 8a, 8b, 8c, 8d, 8e, depicts the permitted space for different parameters, that is allowed by MEG 2016 bound by MEG collaboration [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

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