{"id":"04672e3a-1ca8-474a-8c88-c2da92205780","arxiv_id":"2507.07970","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Including non-holomorphic soft terms in the RGE running of GMSB with adjoint messengers enlarges the allowed parameter space, keeps the stau non-tachyonic at small hypercharge messenger coupling, and can reduce SUSY contributions to muon g-2 by up to about 50 x 10^-10.","lead":"A supersymmetry model paper adds non-holomorphic soft terms to gauge-mediated breaking with adjoint messengers and runs them in the renormalization group. It reports that these terms keep the right-handed stau from becoming tachyonic, shift sparticle masses by up to tens of TeV, boost the Higgs mass by up to 80 GeV, and can suppress muon g-2 contributions enough to keep light sleptons and gauginos viable.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (2.9), the RGE engine behind the stau/Higgs/g-2 claims, is dimensionally inconsistent as printed: A'_f is a mass, while |mu'|^2 is mass^2, so the NH terms cannot be implemented literally; the numerical results are unverifiable until this is corrected.","rationale":"The reader's conditional verdict focused on the arbitrariness of the Eq. (2.4) boundary condition. I agree that is a real limitation, but the more immediate blocker is Eq. (2.9): as printed, its NH terms have incompatible mass dimensions, so the numerical output cannot be reproduced from the paper. This is an internal consistency check independent of any UV-completion assumption. If the equation is merely a typesetting error and the code uses |A'|^2, the central effects may survive partly, but the sign structure changes and the reported numbers must be recomputed. I therefore retain the reader's CONDITIONAL verdict, but with a different, sharper justification. I am not accusing any author of error in intention; the issue is that the manuscript, as written, does not provide a dimensionally coherent basis for the calculation.","tokens_in":18471,"tokens_out":13427,"duration_ms":157956,"concrete_test":"Obtain the modified SARAH/SPheno model file or reconstruct it with SARAH, and inspect the RGE term for m^2_tauR (Eq. 2.9). Check whether the code uses 2 y_tau^2 (A'_tau - 2|mu'|^2) as printed, or the dimensionally consistent 2 y_tau^2 (|A'_tau|^2 - 2|mu'|^2). Then rerun benchmark Point 1 of Table 1 with the corrected term. If the resulting Delta m_stauR or Delta m_h changes by more than about 50%, or if the physical stau mass-square becomes tachyonic, the paper's quantitative claims are not reproducible as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (2.9) is the essential input for the headline effects (positive m^2_tauR at small Lambda5, Delta m_stauR ~ 25 TeV, Delta m_h ~ 80 GeV, Delta(Delta a_mu) ~ -50e-10). As printed, each NH term is dimensionally inconsistent: A'_t, A'_b, A'_tau are mass parameters (Eq. 2.6), while |mu'|^2 is mass^2. For example, dm^2_tauR/dt contains 2 y_tau^2 (A'_tau - 2 |mu'|^2), where the first term has dimension mass but must contribute to a mass-squared RGE. Either the intended term is |A'_tau|^2 (or A'^2), or the equation cannot be used in a SPheno run. The sign and magnitude of this term are not a minor issue: if the correct form is |A'_tau|^2 - 2|mu'|^2, then mu' enters quadratically and can offset or reverse the A' effect, directly threatening the claim that NH terms keep the stau mass-square positive. A secondary but related weakness is Eq. (2.4): the NH couplings are imposed at M_Mess with random signs and O(1) coefficients, and Eq. (2.5) has no RG source, so all low-scale effects inherit this assumed boundary condition.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18810,"tokens_out":8080,"duration_ms":91519,"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":[{"comment":"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.","section":"2.1, Eq. (2.9)"},{"comment":"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.","section":"Abstract, 4.1, 6"},{"comment":"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.","section":"2, Eqs. (2.4)-(2.5)"}],"minor_comments":[{"comment":"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.","section":"Figure 1 caption and Section 4"},{"comment":"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.","section":"Eq. (2.9)"},{"comment":"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.","section":"Section 5"},{"comment":"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.","section":"Table 1"},{"comment":"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.","section":"Eq. (2.2-b)"}],"recommendation":"major_revision","confidential_remarks":"The main technical blocker is the dimensionally inconsistent Eq. (2.9), which is the engine for the headline results. The authors should be asked to provide the corrected RGEs and to confirm that the numerical implementation matches them; otherwise the quantitative claims cannot be checked. The three-orders-of-magnitude discrepancy between the abstract and the body for the stau mass shift must also be resolved before any further consideration. I do not see a reason to reject the paper outright, because the qualitative mechanism is plausible and the framework is within the scope of a phenomenological journal, but the revision needs to address the internal consistency of the equations and the claimed numbers."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—\n\nThe genuinely new thing here is that Nis and Un put non-holomorphic soft terms directly into the RGE running from the messenger scale down, instead of adding them only at the low scale as most earlier GMSB with adjoint messengers papers did. That is a legitimate extension, and the qualitative mechanism they push—NH terms can keep the right-handed stau mass-square positive for small Λ5 and can suppress the SUSY contribution to muon g−2—is plausible from the structure of the RGEs. They also deserve credit for being upfront that the NH couplings have no RG source, so the boundary condition in Eq. (2.4) completely determines their low-scale values.\n\nThe soft spots are serious, though. The biggest is Eq. (2.9), which is dimensionally inconsistent as printed: A′τ has dimension mass, |μ′|² has dimension mass², and the RGE for m²τR subtracts them. That cannot be what SPheno ran. Either the intended term is |A′τ|² (or something else), or the manuscript needs to show the correct equation before the numerical claims can be checked. This is the equation behind the 25 TeV stau shift, the 80 GeV Higgs shift, and the −50×10⁻¹⁰ g−2 suppression, so it is not a typo you can wave away.\n\nTwo more issues. The abstract says a 25 GeV difference in the right-handed stau mass; the full text and Table 1 say 25 TeV. That is a factor of a thousand, and it has to be fixed. The mass-comparison plots in Figures 3–5 deliberately exclude the small-Λ5 region where the NH effects are largest, so the headline effect is not actually displayed. And the random signs and O(1) coefficients in Eq. (2.4) mean a different UV completion could remove the whole effect; the authors note the boundary assumption but don't test its sensitivity.\n\nWho is this for? People working on GMSB variants and on non-holomorphic soft terms. The idea is worth a serious referee, and the paper deserves a chance after revision, but I would not take the numbers at face value until the authors release the modified SARAH/SPheno code and the scan data. Send it out, but with a strong request for those artifacts and a pointed question about Eq. (2.9).","headline":"Plausible mechanism, but the central RGE is dimensionally inconsistent as printed and the quantitative claims are unverifiable without code or data.","tokens_in":19342,"tokens_out":3790,"would_cite":false,"duration_ms":35685,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["gauge mediated supersymmetry breaking","adjoint messengers","non-holomorphic soft terms","stau mass","Higgs boson mass","muon g-2","renormalization group evolution","MSSM"],"falsifier":"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.","tokens_in":18220,"feed_emoji":"⚛️","tokens_out":13254,"duration_ms":135363,"temperature":0.7,"pith_summary":"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.","feed_headline":"Neglected terms shift staus by 25 TeV and lift the Higgs by 80 GeV","feed_subtitle":"Non-holomorphic terms keep stau masses positive at tiny hypercharge coupling and make light sleptons consistent with the muon g-2 bound.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"derives the adjoint-messenger GMSB gaugino and sfermion soft masses in terms of $\\Lambda_{5,3,8}$ and $M_{\\rm Mess}$ used as the holomorphic baseline.","marker":"[19]"},{"why":"identifies the tachyonic and too-light right-handed stau problem at small $\\Lambda_5$ that the paper's NH mechanism is claimed to solve.","marker":"[21]"},{"why":"establishes the large positive SUSY contributions to muon g-2 in GMSB-ADJ that the paper claims NH terms can reduce.","marker":"[22]"},{"why":"provides the higher-dimensional operator analysis and $1/M$ suppression estimate behind the NH boundary condition in Eq. (2.4).","marker":"[27]"},{"why":"is the earlier GMSB study of non-holomorphic soft terms that this work extends by imposing them at the messenger scale and running them.","marker":"[31]"},{"why":"supplies the standard one-loop gaugino and two-loop scalar GMSB mass formulas used to set the holomorphic soft spectrum.","marker":"[44]"},{"why":"gives the updated Standard-Model value of the muon anomalous magnetic moment whose small discrepancy defines the target for NH suppression.","marker":"[62]"},{"why":"reports the experimental muon g-2 measurement used to impose the constraint $\\Delta a_\\mu \\leq 6.6 \\times 10^{-10}$ in the scans.","marker":"[63]"}],"fun_headline_variants":["Non-holomorphic terms rescue stau, boost Higgs by 80 GeV","GMSB adjoint: stau saved, Higgs up 80 GeV, g-2 down","Non-holomorphic terms: stau mass positive, g-2 bound eased","Adjoint messengers: 80 GeV Higgs lift from non-holomorphic"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Non-holomorphic terms rescue stau, boost Higgs by 80 GeV","GMSB adjoint: stau saved, Higgs up 80 GeV, g-2 down","Non-holomorphic terms: stau mass positive, g-2 bound eased","Adjoint messengers: 80 GeV Higgs lift from non-holomorphic"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000247,"raw_usage":{"total_tokens":1705,"prompt_tokens":1270,"completion_tokens":435,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":886,"completion_tokens_details":{"reasoning_tokens":347}},"tokens_in":886,"tokens_out":435,"duration_ms":4497,"temperature":1.0,"reasoning_tokens":347,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:28:09.064175+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"A practical GMSB model for explaining the muon (g-2) with gauge coupling unification","cited_arxiv_id":"1311.1906","evidence_quote":"derives the adjoint-messenger GMSB gaugino and sfermion soft masses in terms of $\\Lambda_{5,3,8}$ and $M_{\\rm Mess}$ used as the holomorphic baseline."},{"cited_title":"Gauge Mediation Models with Adjoint Messengers","cited_arxiv_id":"1609.02124","evidence_quote":"identifies the tachyonic and too-light right-handed stau problem at small $\\Lambda_5$ that the paper's NH mechanism is claimed to solve."},{"cited_title":"Muon g-2 in GMSB with Adjoint Messengers","cited_arxiv_id":"1612.02376","evidence_quote":"establishes the large positive SUSY contributions to muon g-2 in GMSB-ADJ that the paper claims NH terms can reduce."}],"review_version":1}