{"id":"adf7a868-b0d3-470b-9a3c-80de8ee9be37","arxiv_id":"1908.00693","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The FeynHiggs NNLL hybrid and the authors' three-loop fixed-order predictions of the MSSM light Higgs mass agree below 10 TeV, and the measured Higgs mass rules out SUSY scales above 12.5 TeV in the heavy-SUSY, no-mixing benchmark.","lead":"This paper compares two independent calculations of the lightest Higgs boson mass in the Minimal Supersymmetric Standard Model: a three-loop fixed-order result and an effective-field-theory hybrid resummation from FeynHiggs. The two agree within about 1 GeV for SUSY scales below 10 TeV, and the measured Higgs mass then bounds the SUSY scale in one benchmark scenario.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed 0.2–1 GeV agreement between the three-loop fixed-order and FeynHiggs NNLL predictions depends on an unquantified DR-to-MS top-quark mass conversion; the paper itself flags such conversions as a source of large shifts.","rationale":"The paper's central claim is a numerical comparison, so the most load-bearing assumption is that the two compared calculations share the same input scheme. They do not: the NNLL curve uses an MS-bar top mass while the fixed-order curve uses a DR-bar top mass. The paper even identifies scheme conversion in its introduction as a source of large shifts in exactly this kind of comparison, yet it never quantifies the conversion between runningMT=1 and runningMT=3. Because M_h depends sensitively on m_t, the observed 0.2-1 GeV difference could be substantially contaminated by the scheme mismatch. The absence of a fixed-order uncertainty band further prevents the reader from judging whether the residual difference is meaningful. I do not think this invalidates the paper; it makes the central agreement claim conditional on a check that is straightforward to perform. The exclusion bound, being based on the FeynHiggs NNLL curve alone, is less affected, so the appropriate verdict remains CONDITIONAL. The reader's weakest_assumption identifies the same issue, so I agree.","tokens_in":13386,"tokens_out":8009,"duration_ms":80966,"concrete_test":"Rerun the Fig. 2 comparison with both curves in the same top-quark scheme. The cleanest check is to convert the DR top mass used in the FHAddSelf insertion to the MS-bar top mass at O(alpha_s) (including MSSM threshold contributions) and repeat the fixed-order run with runningMT=1, keeping all other flags identical; alternatively, use FeynHiggs itself to estimate the scheme sensitivity by running the 1+2-loop fixed-order mode with runningMT=1 versus runningMT=3 and recording the resulting shift in M_h at a few MSUSY values (e.g. 2, 5, 10 TeV). If the difference between the NNLL and fixed-order curves below 10 TeV changes by more than about 0.5 GeV under this conversion, the central agreement claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section 4 the two predictions being compared use different top-quark mass schemes. The FeynHiggs NNLL result is obtained with runningMT=1 (top quark mass in the SM MS-bar scheme at NNLO), while the three-loop O(alpha_t alpha_s^2) fixed-order insertion via FHAddSelf uses runningMT=3 (DR-bar top mass). The paper provides no conversion between m_t^DR and m_t^MS at the chosen renormalization scale mu_r = MSUSY. This matters because the introduction (Section 1) explicitly lists scheme conversion of input parameters as one of the three sources of 'large shifts due to uncontrolled higher-order terms' in comparisons of FeynHiggs with other codes. Since M_h is highly sensitive to m_t, a 1-2 GeV difference between MS and DR top masses can shift M_h by an amount comparable to the claimed agreement band of 0.2-1 GeV. Hence the lower panels of Figs. 2-4 may be measuring the scheme mismatch rather than genuine agreement between the fixed-order and NNLL calculations. The lack of an uncertainty estimate for the fixed-order curve makes the raw difference impossible to interpret without first controlling this effect.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript compares the authors' recent three-loop fixed-order O(alpha_t alpha_s^2) calculation of the lightest MSSM Higgs-boson mass with the NNLL EFT-hybrid prediction implemented in FeynHiggs 2.14.3. In the heavy-SUSY single-scale benchmark with tan(beta)=10, A_f=0 and zero stop mixing, the two predictions are stated to agree to within about 0.2-1 GeV for MSUSY below roughly 10 TeV. The paper also reports that the agreement improves when a gluino threshold or a non-zero stop mixing is introduced, and it uses the combined CMS/ATLAS measurement M_h^exp = 125.09 +/- 0.24 GeV to derive an upper bound on the SUSY scale, concluding that the region MSUSY > 12.5 +/- 1.2 TeV is excluded in the considered scenario.","tokens_in":13638,"tokens_out":8167,"duration_ms":78759,"significance":"If accepted, the comparison is a useful cross-check between a diagrammatic three-loop fixed-order calculation and a publicly available resummed hybrid code in a region not covered by the earlier H3m benchmark, and the derived upper bound on MSUSY is a concrete phenomenological statement. The paper is commendably explicit about the FeynHiggs flag settings and about the region where large fixed-order logarithms spoil the result. However, the central numerical claims rest on an unquantified top-quark scheme mismatch and on an uncertainty estimate that applies to only one of the two curves, so the agreement and the exclusion bound require qualification before they can be taken at face value.","major_comments":[{"comment":"The comparison is made between two calculations that use different top-quark mass schemes. The FeynHiggs NNLL result is obtained with runningMT=1 (SM MS-bar top mass at NNLO), while the three-loop fixed-order insertion via FHAddSelf uses runningMT=3 (DR-bar top mass), at the common renormalization scale mu_r = MSUSY. No conversion between m_t^MS(mu_r) and m_t^DR(mu_r) is provided, and Section 1 itself lists scheme conversion of input parameters as a source of potentially large shifts from uncontrolled higher-order terms. For MSUSY at the TeV scale the MS-DR difference in m_t is of order several GeV and can shift M_h by an amount comparable to the claimed 0.2-1 GeV agreement. Please quantify this scheme shift, or perform the comparison with a single top-quark mass scheme.","section":"Section 4, top-quark mass scheme (runningMT=1 vs runningMT=3)"},{"comment":"The blue band shown in the figures is the FHUncertainties estimate for the FeynHiggs NNLL prediction, as stated in the text, but the red three-loop fixed-order curve is shown without any uncertainty estimate. The statement that the 0.2 GeV difference is 'within the theoretical uncertainty (blue band)' is therefore not valid: that band does not apply to the fixed-order calculation, and no combined or fixed-order-specific uncertainty is given. Without an uncertainty estimate for the red curve, the agreement claim of 0.2-1 GeV has no well-defined significance.","section":"Section 4 and lower panels of Figs. 2-4"},{"comment":"The derivation of the bound MSUSY > 12.5 +/- 1.2 TeV does not state explicitly which M_h prediction is used for the contours in Figs. 5 and 6. This distinction matters because above 10 TeV the fixed-order and NNLL curves differ by up to tens of GeV. If the contours are based on the NNLL curve, the sentence saying that the region where the three-loop results 'blow up' is excluded by the measured Higgs mass is misleading, since an unreliable fixed-order prediction cannot by itself exclude a region; if the contours are based on the fixed-order curve, the bound is not trustworthy above 10 TeV. Please state the curve used and define the exclusion using the appropriate prediction and its uncertainty.","section":"Section 4, Figs. 5-6 and the exclusion bound"}],"minor_comments":[{"comment":"The text says 'MSUSY must be at most 12.5 +/- 1.2 GeV'; the unit should be TeV.","section":"Section 4, paragraph after Fig. 6"},{"comment":"For reproducibility, the values of the input parameters not controlled by the listed FeynHiggs flags (in particular the top-quark mass, alpha_s, and any FeynHiggs defaults used for the MSSM parameters) should be listed explicitly.","section":"Section 4, flag settings"},{"comment":"The caption refers to 'the NNLO results of FeynHiggs' while the text and other captions describe the same curves as NNLL; the terminology should be made consistent.","section":"Figure 4 caption"},{"comment":"References [14] and [35] are duplicates of the same ATLAS/CMS combined measurement and one should be removed.","section":"References"},{"comment":"The quoted 12.5 +/- 1.2 TeV uncertainty is associated with the zero-mixing curve only; for other values of X_t/MSUSY no uncertainty is shown, and the text should state that the bound with its uncertainty applies to the X_t=0 case.","section":"Section 4, exclusion bound for non-zero mixing"}],"recommendation":"major_revision","confidential_remarks":"The central cross-check is plausible and worth publishing after revision, but the numerical agreement claim and the exclusion bound both depend on choices that are currently unquantified or unspecified. The most important fix is to control the top-quark scheme conversion and to assign an uncertainty to the fixed-order curve. The self-citation to the authors' earlier work is appropriate here because the present paper benchmarks that work against an independent code; I do not see a circularity problem."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nYou should know about this one because it is a direct cross-check of the authors' own three-loop fixed-order calculation of the lightest MSSM Higgs mass against the NNLL EFT-hybrid prediction of FeynHiggs 2.14. They find agreement within 0.2–1 GeV for MSUSY below about 10 TeV in the heavy-SUSY benchmark, and they turn that into an exclusion of MSUSY above 12.5 ± 1.2 TeV using the measured Higgs mass. That is the headline.\n\nThe comparison is genuinely new, and it does some things right. The previous checks of their three-loop result were against H3m at low scales; here they go up to 20 TeV, and the figures are clear. Using FeynHiggs as a benchmark is sensible, and the inclusion of a gluino-mass threshold and non-zero Xt makes the scan more informative. The exclusion contours in Fig. 6 are a useful addition, even if not the main point.\n\nThe soft spots are real but not fatal. The most serious is the unquantified DR vs. MS top-quark mass scheme mismatch. In Section 4 they run the FeynHiggs NNLL with runningMT=1 (MS-bar) and the FHAddSelf insertion with runningMT=3 (DR-bar), and they do not give any conversion between the two. The introduction itself warns that scheme conversion is a source of large shifts. Since Mh is sensitive to m_t, a 1% scheme difference can shift Mh by about a GeV, which is the same size as the claimed agreement band. So the lower panels of Figs. 2–4 could in principle be showing the scheme mismatch rather than true agreement. The paper does not provide an uncertainty band for the fixed-order curve, which makes the raw difference hard to interpret. This needs to be addressed: either convert the top mass explicitly, or estimate the shift and add it to the error budget.\n\nThe exclusion bound also has a soft spot: the quoted 12.5 ± 1.2 TeV has an uncertainty that is not derived. The purple lines in Fig. 6 presumably come from the FeynHiggs uncertainty band, but the text does not say how that is propagated. And there are a couple of typos where TeV is written as GeV in Section 4. Minor, but sloppy.\n\nIf the scheme issue is resolved, the central agreement claim probably survives. The paper is worth a serious referee, not for the method (it is all established) but for the cross-check itself. I would send it to peer review, asking for an explicit treatment of the top-quark mass scheme and a proper uncertainty estimate on the three-loop curve.\n\nBest,\n[Name]","headline":"Useful cross-check of a three-loop fixed-order MSSM Higgs mass calculation against FeynHiggs NNLL, but the unquantified DR/MS top-mass scheme mismatch leaves the claimed 0.2–1 GeV agreement without a clean interpretation.","tokens_in":14158,"tokens_out":5594,"would_cite":false,"duration_ms":51975,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that two independent high-precision calculations of the lightest MSSM Higgs mass agree to about 0.2–1 GeV for SUSY scales below 10 TeV, and that the measured Higgs mass excludes scales above $12.5\\pm1.2$ TeV in the…","keywords":["MSSM Higgs mass","three-loop fixed order","NNLL resummation","EFT hybrid calculation","heavy SUSY limit","stop mixing","SUSY scale bound","Higgs boson mass"],"falsifier":"Rerun the comparison with the top-quark mass in the same renormalization scheme on both sides — for example, feed a $\\overline{\\text{DR}}$ top mass into the resummation or an $\\overline{\\text{MS}}$ top mass into the three-loop self-energy insertion — and check whether the difference stays inside the claimed 0.2–1 GeV band for $M_\\text{SUSY}<10$ TeV. If the shift moves by several GeV, the agreement is largely a scheme artifact; if it stays within the band, the cross-check survives its weakest point.","tokens_in":13171,"feed_emoji":"⚛️","tokens_out":11047,"duration_ms":97101,"temperature":0.7,"pith_summary":"This paper establishes that two independent ways of computing the lightest Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM) — a direct three-loop diagrammatic calculation and a hybrid calculation that resums large logarithmic corrections — give consistent answers in the range where both should be trustworthy. In a simplified benchmark with a single supersymmetric mass scale and vanishing stop mixing, the two predictions agree to within about 0.2–1 GeV for SUSY scales below 10 TeV. The paper also turns the measured Higgs mass into a constraint on the model: in this benchmark, SUSY scales above $12.5\\pm1.2$ TeV are excluded. The significance is that two methodologically different high-precision calculations cross-check each other, and that LHC data can already bound the scale of supersymmetry in this scenario.","feed_headline":"Two paths to the MSSM Higgs mass agree below 10 TeV","feed_subtitle":"A three-loop calculation and a resummed-log hybrid match to ~1 GeV; 12.5 TeV SUSY scales are ruled out.","key_machinery":"The machinery is the pole equation for the lightest CP-even Higgs mass, $p^2 - m_h^2 + \\sum_{\\ell=1}^3 \\hat{\\Pi}^{(\\ell)}_{hh}=0$, evaluated in the heavy-SUSY limit where all supersymmetric masses are set to a common scale $M_\\text{SUSY}$ and the low-energy effective theory is the Standard Model. The fixed-order side is assembled from a basis of 33 three-loop master integrals (the irreducible Feynman integrals obtained after integration by parts); the hybrid side adds a resummation shift $\\Delta^\\text{log}_{hh}$ that subtracts the logarithms already present in the fixed-order self-energies so they are not counted twice. That subtraction, together with the renormalization-scheme choices for the top quark, is what makes the comparison between the two approaches meaningful.","core_discovery":"On its own terms, the paper's central numerical discovery is a cross-check: the three-loop fixed-order prediction of $\\mathcal{O}(\\alpha_t\\alpha_s^2)$ and the NNLL resummed prediction of the hybrid approach for $M_h$ agree to within about $0.2$ GeV in the interval $2.2 \\lesssim M_\\text{SUSY} \\lesssim 7.4$ TeV and to at most about 1 GeV below 10 TeV, for a degenerate heavy-SUSY benchmark with $X_t=0$ and $\\tan\\beta=10$. The agreement is not limited to one parameter point: setting the gluino mass to 1.5 TeV or increasing the stop mixing parameter to $X_t/M_\\text{SUSY}\\approx 1.5$ keeps the difference small while changing the shape of the mass curve. Above 10 TeV the fixed-order result accumulates large logarithms of $M_\\text{SUSY}/M_t$ and diverges from the resummed result, growing to tens of GeV by 40 TeV; the paper argues this region is experimentally irrelevant because the combined LHC mass measurement, $M_h^\\text{exp}=125.09\\pm0.24$ GeV, already excludes $M_\\text{SUSY}>12.5\\pm1.2$ TeV in the considered scenario.","pith_inferences":["Editorial inference: a scheme-uniform rerun of the top-quark mass is the cheapest decisive check of whether the 0.2–1 GeV agreement is physical or an artifact of the $\\overline{\\text{MS}}$/$\\overline{\\text{DR}}$ conversion.","Editorial inference: the same comparison could be extended beyond the degenerate benchmark to non-universal spectra where $M_A$ differs from the sfermion scale, since the fixed-order three-loop calculation is claimed to be valid across the whole MSSM parameter space.","Editorial inference: a future combined Run-2 measurement with a smaller uncertainty would, if the bound holds, push the excluded SUSY scale downward and sharpen the tension with naturalness.","Editorial inference: checking negative values of $X_t/M_\\text{SUSY}$ would test whether the improved agreement near +1.5 is symmetric or tied to the sign of the stop mixing angle."],"forward_implications":["Below about 10 TeV in this benchmark, the two high-precision predictions for $M_h$ can be used interchangeably at the 1 GeV level.","Above 10 TeV, the fixed-order three-loop result accumulates large logarithms and should not be used; the resummed hybrid result is the reliable one there.","In the heavy-SUSY scenario with $\\tan\\beta\\gtrsim 10$, the measured Higgs mass excludes $M_\\text{SUSY}>12.5\\pm1.2$ TeV.","Increasing $|X_t/M_\\text{SUSY}|$ up to about 1.5 reduces the difference between the two calculations by roughly a factor of seven compared with $X_t=0$.","The point $X_t/M_\\text{SUSY}=2.4$ is a maximum of $M_h$ at every $M_\\text{SUSY}$, which makes it the reference point for the minimal required SUSY scale."],"supporting_citations":[{"why":"Supplies the three-loop $\\mathcal{O}(\\alpha_t\\alpha_s^2)$ fixed-order calculation that is the first object of the comparison.","marker":"[34]"},{"why":"Provides the hybrid EFT implementation, including the NNLL resummation, against which the fixed-order result is checked.","marker":"[67]"},{"why":"Shows that the hybrid approach agrees with pure EFT after scheme and subloop corrections, supporting its use at large SUSY scales.","marker":"[53]"},{"why":"Gives the NNLL resummation formalism and the gluino-mass dependence used to set up the additional-scale scenario.","marker":"[69]"},{"why":"Supplies the combined LHC Higgs-mass measurement $125.09\\pm0.24$ GeV that drives the SUSY-scale exclusion.","marker":"[14]"},{"why":"Estimates the critical SUSY scale near 1.2 TeV below which fixed order is more accurate, motivating the comparison range.","marker":"[40]"},{"why":"Provides an independent three-loop code prediction used to validate the fixed-order calculation at low SUSY scales.","marker":"[33]"},{"why":"Used to evaluate numerically the three-loop master integrals in the fixed-order self-energies.","marker":"[63, 64]"},{"why":"Used for the evanescent $O(\\varepsilon)$ contributions of the master integral $I_{211100}$.","marker":"[65]"}],"fun_headline_variants":["MSSM Higgs: two routes to the same mass below 10 TeV","SUSY scale >12.5 TeV ruled out by LHC Higgs mass","Three-loop and resummed Higgs mass match to ~1 GeV","Fixed-order vs EFT: Higgs mass agrees under 10 TeV","Higgs mass confines SUSY scale below 12.5 TeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the unquantified conversion between the $\\overline{\\text{DR}}$ top-quark mass used in the three-loop insertion and the $\\overline{\\text{MS}}$ top-quark mass used in the hybrid resummation does not shift $M_h$ by as much as the claimed 0.2–1 GeV agreement; the paper itself notes that scheme conversion can produce large uncontrolled shifts.","fun_headline_variants_meta":{"raw":{"variants":["MSSM Higgs: two routes to the same mass below 10 TeV","SUSY scale >12.5 TeV ruled out by LHC Higgs mass","Three-loop and resummed Higgs mass match to ~1 GeV","Fixed-order vs EFT: Higgs mass agrees under 10 TeV","Higgs mass confines SUSY scale below 12.5 TeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001195,"raw_usage":{"total_tokens":4948,"prompt_tokens":981,"completion_tokens":3967,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":3867}},"tokens_in":597,"tokens_out":3967,"duration_ms":27267,"temperature":1.0,"reasoning_tokens":3867,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:37:41.326691+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the comparison with the top-quark mass in the same renormalization scheme on both sides — for example, feed a $\\overline{\\text{DR}}$ top mass into the resummation or an $\\overline{\\text{MS}}$ top mass into the three-loop self-energy insertion — and check whether the difference stays inside the claimed 0.2–1 GeV band for $M_\\text{SUSY}<10$ TeV. If the shift moves by several GeV, the agreement is largely a scheme artifact; if it stays within the band, the cross-check survives its weakest point.","supporting_citations":[],"review_version":1}