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REVIEW 3 major objections 5 minor 63 references

Non-holomorphic Contributions in GMSB with Adjoint Messengers

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Non-holomorphic soft terms, usually neglected because they are higher-order, can shift the right-handed stau mass by about 25 TeV, raise the SM-like Higgs mass by up to 80 GeV, and cut SUSY contributions to muon g-2 by about 50 x 10^-10.

desk verdict Plausible mechanism, but the central RGE is dimensionally inconsistent as printed and the quantitative claims are unverifiable without code or data. read the letter →

arxiv 2507.07970 v1 pith:VIIQZ4BV submitted 2025-07-10 hep-ph

Busra Nis , Cem Salih Un This is my paper
classification hep-ph
keywords gaugemediatedsupersymmetrybreakingadjointmessengersnon-holomorphicsofttermsstaumassHiggsbosonmuong-2renormalizationgroupevolutionMSSM
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 tries to establish that non-holomorphic supersymmetry-breaking terms, although they are generated only at higher loop order and are suppressed by the messenger mass, are a decisive ingredient in gauge-mediated SUSY breaking with adjoint messengers. The authors impose these terms at the messenger scale with the size $A', \mu' \sim (1/M_{\rm Mess})\sum_i \Lambda_i^2$, evolve them through the renormalization-group equations together with the ordinary soft masses, and find that they open a previously tachyonic region: the right-handed stau mass-square stays positive even when the hypercharge messenger coupling $\Lambda_5$ is as small as $10^{-7}$ GeV. In this enlarged parameter space the non-holomorphic terms can shift the right-handed stau mass by about 25 TeV, the stop mass by about 15 TeV, and the sbottom mass by 6-7 TeV, and can raise the SM-like Higgs mass by up to about 80 GeV while reducing SUSY contributions to muon g-2 by about $50 \times 10^{-10}$. If this is right, switching these terms off at the messenger scale is not a harmless approximation; it is what creates the apparent need for very heavy sleptons, and models with light sleptons and gauginos can remain consistent with the current muon g-2 results.

What carries the argument

The central object is the non-holomorphic soft sector: the wrong-Higgs trilinear couplings $A'_i$ and the non-holomorphic Higgsino mass $\mu'$, which appear in the soft Lagrangian as sfermion couplings to the 'wrong' Higgs doublet. These couplings are generated by higher-dimensional operators with magnitude $A', \mu' \sim (1/M_{\rm Mess})\sum_i \Lambda_i^2$, and because their RGEs have no source term, setting them to zero at the messenger scale would leave them zero at all scales. The paper keeps them small but non-zero, runs them to the weak scale, and lets them enter the sfermion mass matrices through $X_{\tilde t}$, $X_{\tilde b}$, $X_{\tilde\tau}$ while also feeding back into the running of the diagonal soft masses. The stau is singled out because its holomorphic SSB mass depends only on $\Lambda_5$, so the NH terms are the only thing that can keep $m^2_{\tilde\tau_R}$ positive when $\Lambda_5$ is small.

What would settle it

Compute the non-holomorphic couplings at the messenger scale in a specific UV completion of the hidden sector: if the operators behind Eq. (2.3) are generated only at higher loop order than assumed, or with a fixed sign relation, the predicted 25 TeV stau shift, 80 GeV Higgs boost, and $-50 \times 10^{-10}$ g-2 shift will not appear. A cleaner experimental falsifier: a future muon g-2 measurement or improved SM calculation that requires a positive new-physics contribution of order $30 \times 10^{-10}$ would contradict the paper's claim that NH terms can suppress SUSY contributions while keeping sleptons and gauginos light.

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Extended reading notes

Core claim

The paper's central claim is that non-holomorphic soft terms turn the stau problem of GMSB-ADJ into a feature. Without the NH terms, the right-handed stau receives its SSB mass only from the $U(1)_Y$ messenger sector, so $\Lambda_5 \lesssim 10^3$ GeV gives tachyonic states and $10^3 \lesssim \Lambda_5 \lesssim 10^5$ GeV gives unacceptably light staus. With NH terms included in the RGEs, $m^2_{\tilde\tau_R}$ can remain positive all the way down to $\Lambda_5 \approx 10^{-7}$ GeV, provided $M_{\rm Mess}$ is roughly $10^8$-$10^9$ GeV in that region and $\Lambda_3$, $\Lambda_8$ are large enough to generate the NH couplings. The same running shifts the spectrum: about 25 TeV on the right-handed stau, up to about 20 TeV on the lightest stau mass eigenstate, 6-7 TeV on the sbottom, about 15 TeV on the stop, and, through the sparticle mixing, changes the SM-like Higgs mass by up to about 80 GeV in the positive direction and about 20 GeV in a small negative region. For muon g-2, the NH terms can reduce the SUSY contribution by about $50 \times 10^{-10}$, so points whose holomorphic version predicts $\Delta a_\mu \approx 40 \times 10^{-10}$ can satisfy the current bound while keeping smuons and Binos relatively light.

Load-bearing premise

The analysis rests on the assumption that, at the messenger scale, the non-holomorphic couplings are as large as the summed squared messenger supersymmetry-breaking scales divided by the messenger mass, with freely random signs; a UV completion that made these couplings smaller or fixed their signs would shrink or reverse the claimed effects.

Editorial extensions

If this is right

  • The small-$\Lambda_5$ region of GMSB-ADJ, previously excluded by tachyonic or too-light staus, becomes viable; there $M_{\rm Mess}$ is bounded to roughly $10^8$-$10^9$ GeV, with $\Lambda_3$, $\Lambda_8$ supplying the NH couplings.
  • NH contributions to sfermion masses are mostly positive and can reach about 25 TeV for the right-handed stau, 15 TeV for the stop, and 6-7 TeV for the sbottom, shifting the whole low-energy spectrum and the decoupling scale $M_{\rm SUSY}$ upward.
  • The SM-like Higgs boson mass can be lifted by up to about 80 GeV through NH-modified stau and sbottom mixing, so points whose holomorphic Higgs mass is 40-70 GeV can satisfy the 123-127 GeV experimental band.
  • SUSY contributions to muon g-2 can be reduced by as much as about $50 \times 10^{-10}$, allowing large-$\tan\beta$ points with $\Delta a_\mu^H \approx 40 \times 10^{-10}$ to pass the current bound while keeping light smuons and Binos viable.
  • In a small region of parameter space the NH effects are negative, lowering sparticle masses by no more than about 1 TeV and the Higgs mass by about 20 GeV, and these points still pass the applied constraints.

Reading between the lines

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

  • An implication the paper leaves implicit: because the NH terms shift the whole decoupling scale, GMSB-ADJ predictions for dark-matter relic density, flavor observables, and collider mass correlations should be recomputed with the NH boundary condition, not with the holomorphic spectrum.
  • A useful cross-check the paper does not perform: build an explicit hidden-sector model that generates the effective operators behind Eq. (2.3) and compute $A'$ and $\mu'$ at the required loop order; that would fix their signs and test whether the large benchmark shifts survive.
  • The scan treats the signs of $A'$ and $\mu'$ as random; if a UV completion fixes them, the allowed $\Lambda_5$-$M_{\rm Mess}$ region and the 25 TeV/80 GeV maxima could shrink substantially, so sign sensitivity is the lever a follow-up should quantify.
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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 / 5 minor

Summary. This paper studies gauge-mediated supersymmetry breaking with adjoint messengers (GMSB-ADJ) and adds non-holomorphic (NH) soft-breaking terms A' and mu' imposed at the messenger scale. The authors take A', mu' ~ sum_i Lambda_i^2 / M_Mess with order-one coefficients and randomly assigned signs, evolve them to low energies with SARAH/SPheno, and report that the NH terms in the RGEs keep the right-handed stau mass-squared positive even for small hypercharge messenger coupling Lambda_5, thereby enlarging the viable parameter space. They further report shifts of up to about 25 TeV in the right-handed stau mass, about 20 TeV in the lightest stau mass eigenstate, 6-7 TeV in the sbottom, about 15 TeV in the stop, up to about 80 GeV in the SM-like Higgs mass, and a reduction of SUSY contributions to muon g-2 by up to about 50 x 10^-10. I note that the abstract quotes 25 GeV and 5 TeV for the same stau quantities, which differs by three orders of magnitude from the full text.

Significance. If the numerical results survive scrutiny, the paper would show that NH terms are not a small correction but a potentially dominant effect in an interesting part of GMSB-ADJ parameter space, connecting to current discussions of m_h and muon g-2. The inclusion of NH terms in the RG evolution, rather than only at the decoupling scale, is a meaningful extension of earlier work and is supported by explicit benchmark points and a scan over the model parameters. However, the central RGE equation as printed is dimensionally inconsistent, and the headline numbers disagree between the abstract and the body. The significance is therefore conditional on correcting these load-bearing issues and verifying that the numerical implementation matches the corrected equations.

major comments (3)
  1. [2.1, Eq. (2.9)] As printed, Eq. (2.9) is dimensionally inconsistent: A'_t, A'_b, and A'_tau are mass parameters from Eq. (2.6), while |mu'|^2 is a mass-squared quantity. For example, dm^2_tauR/dt contains 2 y_tau^2 (A'_tau - 2|mu'|^2), where the first term has mass dimension and the second has mass-squared dimension. The same issue appears in all five lines of Eq. (2.9). This equation drives the claimed stau-mass positivity, the 25 TeV mass shifts, the 80 GeV Higgs-mass shift, and the g-2 suppression, so the numerical results are not verifiable until the intended form is specified. If the correct term is |A'_tau|^2 or (A'_tau)^2, the sign and magnitude of the A' contribution change relative to the mu' contribution, and the stated conclusion that NH terms keep the stau mass-squared positive may be affected. Please correct Eq. (2.9), state the exact RGE implementation used in SARAH/SPheno, and confirm that the reported results follow from a dimensionally consistent set of equations. In addition, the line for dm^2_bR/dt appears to contain A'_t where A'_b is expected.
  2. [Abstract, 4.1, 6] The abstract states that the NH terms produce about 25 GeV difference in the right-handed stau mass and about 5 TeV difference in the lightest stau mass eigenstate, while Sections 4.1 and 6 report about 25 TeV and about 20 TeV, respectively. These are numerically different claims by three orders of magnitude for the first quantity. Since these numbers are the central quantitative results of the paper, they must be reconciled in a revision, and the benchmark points in Table 1 should be checked against the final quoted values.
  3. [2, Eqs. (2.4)-(2.5)] The NH terms have no growing RG source in Eq. (2.5): if A'_i and mu' are set to zero at M_Mess, they remain zero at all scales. Therefore all low-scale NH effects are determined entirely by the assumed boundary condition in Eq. (2.4), including order-one coefficients and randomly assigned signs. The claimed small-Lambda_5 stau positivity, the large mass shifts, the 80 GeV Higgs-mass enhancement, and the -50 x 10^-10 shift in muon g-2 all inherit this assumption. The paper should either scan over the O(1) coefficients, or demonstrate with a concrete test (e.g., varying the coefficients in a fixed interval and comparing fixed versus random signs) that the headline effects are robust to this choice. Without such a test, the quantitative claims should be framed as scenario-dependent consequences of the assumed boundary condition rather than model-independent predictions.
minor comments (5)
  1. [Figure 1 caption and Section 4] The caption and the beginning of Section 4 refer to “the right planes” twice, where the intended comparison is between left and right panels. Please correct the figure caption and the corresponding text.
  2. [Eq. (2.9)] In addition to the dimensional issue, the line for dm^2_bR/dt appears to use A'_t in the bracket where A'_b is the natural NH coupling for the b-right field. Please verify whether this is a typographical error or a genuine feature of the implementation.
  3. [Section 5] The text says the bound is “Delta a_mu <= 6.6 x 10^10”, which should read 10^-10. Also, the notation Delta a_mu is used both for the SUSY contribution (constrained to be between 0 and 6.6 x 10^-10 in Section 3) and for the anomaly Delta a_mu^exp - Delta a_mu^SM in Section 5; please use distinct symbols or clarify the definitions.
  4. [Table 1] The caption contains the sentence “All points are selected to be consistent with the experimental constraints…” twice, and the phrase “the red color emphasize” should be “emphasizes”. These are minor presentation issues but should be cleaned up.
  5. [Eq. (2.2-b)] The expressions for the SSB scalar masses would benefit from an explicit statement of the hypercharge normalization used for U(1)_Y, since the relative factors between m^2_E and the other scalar masses are important for the stau-mass discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the non-holomorphic effects are computed outputs of stated boundary conditions and scans, not fitted to the claimed stau, Higgs, or g-2 results.

full rationale

The derivation chain is input-to-output rather than output-to-input. The soft masses and gaugino masses at the messenger scale are fixed by Eqs. (2.2-a,b); the non-holomorphic couplings A' and mu' are set at the messenger scale by the stated estimate Eq. (2.4), with random signs as an input choice; and all low-scale quantities are then obtained by RG evolution through Eqs. (2.5) and (2.9) and by SPheno/SARAH spectrum and observable computation. Nothing in this chain is fitted to the stau mass, the SM-like Higgs mass, or Delta a_mu; the headline numbers (25 TeV stau shift, ~80 GeV Higgs shift, ~-50e-10 g-2 shift) are differences between two otherwise identical calculations with and without the NH terms, i.e., computed outputs. The NH boundary condition is an assumption rather than a derived prediction, and because the homogeneous RGEs (2.5) have no growing source, the low-scale NH values are determined entirely by that boundary condition; that makes the phenomenological results assumption-dependent, but it is not circular. Self-citations [21,22,36] supply background for the GMSB-ADJ class and earlier NH studies, while the framework also rests on external references [18,19,31-39]; the central claims do not reduce to an unverified self-citation or to a uniqueness theorem imported from the authors. A separate concern is that Eq. (2.9) as printed contains terms of different mass dimension (A'_i has mass dimension one while |mu'|^2 has mass dimension two), which would prevent literal implementation; this is a correctness/verifiability issue, not a circularity. No circular step meeting the quote-and-reduction standard was found.

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

The central claims depend on the assumed size and sign of the non-holomorphic couplings at the messenger scale, and on the one/two-loop RGEs. No new particles are introduced. The scan parameters are listed as free parameters.

free parameters (6)
  • Lambda_5 = 10^-7 to 10^7 GeV (scanned)
    Messenger mass-splitting parameter for U(1)_Y adjoint (5+5bar) messengers; the small-Lambda5 region is the focus of the stau claim. Chosen by scan, not fitted.
  • Lambda_3 = 10^-7 to 10^7 GeV (scanned)
    SU(2)_L adjoint messenger parameter. Required to be larger than about 10^4 GeV to generate large NH terms in the small-Lambda5 region.
  • Lambda_8 = 10^-7 to 10^7 GeV (scanned)
    SU(3)_C adjoint messenger parameter. Large values are needed to satisfy squark and gluino mass bounds.
  • M_Mess = 10^6 to 10^16 GeV (scanned)
    Common messenger mass scale. Small values (below about 10^11 GeV) are needed to induce sizeable NH terms.
  • tan(beta) = 1.2 to 60 (scanned)
    Ratio of Higgs VEVs. NH sbottom and stau mixing effects grow with tan(beta).
  • sign(A'_0), sign(mu') = Random +1 or -1
    Signs of the non-holomorphic terms are not determined by the framework and are assigned randomly, directly controlling whether contributions raise or lower sparticle masses and g-2.
assumptions (5)
  • domain assumption The GMSB-ADJ superpotential of Eq. (2.1) with M5=M3=M8=M_Mess and the standard one/two-loop GMSB SSB mass formulas (Eqs. 2.2-a,b) are valid.
    These formulas are taken from prior GMSB-adjoint literature [18,19] and the present authors' earlier work [21,22]. The complete adjoint representation is assumed to avoid anomalies.
  • ad hoc to paper The NH term boundary condition A', mu' ~ (1/M_Mess) sum_i Lambda_i^2 (Eq. 2.4) with order-one coefficients holds at the messenger scale.
    Eq. (2.4) is an order-of-magnitude estimate from higher-dimensional operators; the paper promotes it to the exact boundary condition and scans over it with random signs.
  • domain assumption The RGEs for the NH terms (Eq. 2.5) and their contributions to sfermion mass-squares (Eq. 2.9) are the correct 1-loop/2-loop evolution used by SPheno.
    These RGEs are cited from the literature; no derivation or validation is shown in this paper.
  • domain assumption There is no MSSM singlet SUSY-breaking field, so NH terms can be treated as ordinary soft terms without reintroducing the hierarchy problem.
    This argument is stated in the Introduction and Conclusion, citing [23,27,28,29].
  • domain assumption The applied experimental constraints (Eq. 3.2) and the muon g-2 bound 0 <= Delta a_mu <= 6.6 x 10^-10 are correct and applicable.
    Bounds are taken from current experimental reviews and the WP25 white paper.

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Cite this review

Pith. "Pith review of Non-holomorphic Contributions in GMSB with Adjoint Messengers." pith.science (2026). https://pith.science/paper/VIIQZ4BV

@misc{pith2026250707970,
  author       = {Pith},
  title        = {Pith review of: Non-holomorphic Contributions in GMSB with Adjoint Messengers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VIIQZ4BV}},
  note         = {Machine review of arXiv:2507.07970}
}
read the original abstract

We consider models of gauge mediated supersymmetry breaking, in which the breaking is transmitted to the visible sector by the messenger fields from the adjoint representation of MSSM's gauge group. We include the non-holomorphic terms induced by the supersymmetry breaking and involve them in the renormalization group evolution. The main impact from the non-holomorphic terms arises in the right-handed stau mass, which requires large hypercharge interactions with the messengers to accommodate non-tachyonic staus. With the non-holomorphic terms, the stau mass-square can remain positive in the renormalization group evolution, even if the hypercharge interactions are small. Although the radiative non-holomorphic contributions enhance the mass spectrum, their effects in the sparticle mixing rather reduce their overall contributions such that we realize about 25 GeV difference in the right-handed stau mass, while the difference is lowered by about 5 TeV in the lightest mass-eigenstate of staus. We realize 6-7 TeV difference in the sbottom mass, and about 15 TeV in the stop mass. These contributions in the sparticle masses also affect the SM-like Higgs boson mass, and we find that the SM-like Higgs boson can be enhanced as much as about 80 GeV. In a small region of the parameter space we also observe negative non-holomorphic contributions which do not exceed about 1 TeV for the sparticles, and 20 GeV for the SM-like Higgs boson. An interesting impact from the non-holomorphic terms happens in the muon g-2 results. We find that the non-holomorphic contributions can provide a significant decreasing in supersymmetric contributions to muon g-2. We realize that the muon g-2 results can be decreased as much as about -50 x 10^-10 by the non-holomorphic contributions, and consequently one can still accommodate light sleptons and gauginos in the spectrum.

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