{"id":"e2d5db73-70aa-4ab3-a729-0797fd5a0894","arxiv_id":"2510.14680","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For the first time, the two-loop Yukawa-induced renormalisation-group running of the Higgs-gluon coupling from D^2H^4 and D H^2 ψ^2 SMEFT operators is computed.","lead":"Particle physicists computed the missing two-loop corrections to how the Higgs boson couples to gluons in the Standard Model Effective Field Theory, completing the running for operators that can appear at tree level. The result sharpens the precision of Higgs-data fits and changes bounds on loosely constrained new-quark interactions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Kinematic cancellation excluding two-loop diagrams with both external Higgs legs on the effective vertex is verified only for pure QCD; the mixed Yukawa-QCD case (Fig. 1c) is unchecked, so Eq. (3.1)'s diagram basis may be incomplete.","rationale":"The reader's weakest_assumption is exactly the point I would press. The cancellation argument is the only place where the completeness of the diagram set is established by a symmetry statement rather than by an explicit evaluation. The reported O(g_s^4) check covers Fig. 1b only, and the text gives no evidence for Fig. 1c. If the mixed Yukawa-QCD diagrams survive, Eq. (3.1) would miss contributions at the same order, so the central claim would fail. I do not think this warrants rejection: the two independent pipelines and the agreement with [96] give reason to expect the argument is correct. But the record should contain an explicit check of the mixed case, or a proof of the symmetry. The factor-1/2 discrepancy with [27] is concerning but it concerns the previously known Yukawa-like operator contributions, not the new class 3/7 terms; it is already acknowledged and does not bear on the kinematic cancellation. Therefore I keep the CONDITIONAL verdict.","tokens_in":17704,"tokens_out":9807,"duration_ms":85400,"concrete_test":"Using the same FeynArts/AMFlow pipeline, generate and compute the UV divergent part of the full set of two-loop gg->H*H diagrams with one O_Ht insertion, both external Higgs legs attached to the operator vertex, and one Yukawa plus one QCD correction (Fig. 1c). If the sum of the 1/epsilon poles is nonzero, the kinematic cancellation fails and Eq. (3.1) is incomplete; if it vanishes to numerical precision (e.g., <10^-8 relative), the exclusion is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. 3 the authors discard all two-loop diagrams in which both external Higgs doublets attach to the effective O_Ht vertex, based on the one-loop triangle argument: the derivative current yields a (p1-p2) factor and the remainder of the diagram is symmetric under p1<->p2, so the product vanishes. This exclusion is load-bearing because it reduces the class-7 calculation to the 24 diagrams counted in the text; if the excluded diagrams contribute, Eq. (3.1) is incomplete. The paper reports an explicit cross-check of the cancellation only for the pure-QCD case (a gluon propagator correction between the two QCD vertices, Fig. 1b). No analogous check is shown for the mixed Yukawa-QCD case (Fig. 1c), where an internal Higgs line and chiral projectors are present. The symmetry argument is less trivial there: the effective vertex connects H and H* (not identical legs), and the Yukawa vertex introduces a preferred fermion direction; the remaining amplitude is not manifestly antisymmetric under p1<->p2. Footnote 2 (vanishing of the pure-QCD class-7 contribution at all loop orders at dimension-six level) rests on the same unverified extension. A nonzero mixed diagram would invalidate the completeness of the 24-diagram set and change the coefficients in Eq. (3.1).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper computes the two-loop renormalization-group contribution to the Wilson coefficient C_HG of the Higgs-gluon operator O_HG in SMEFT, at order g_s^2/(16π^2)^2 and proportional to third-generation Yukawa couplings, induced by Warsaw-basis class 7 (ψ^2 H^2 D) and class 3 (H^4 D^2) operators. The final expression, Eq. (3.1), combines these new terms with earlier four-quark [24] and Yukawa-like [27] contributions, and is claimed to complete the two-loop Yukawa-induced running of C_HG for operators that can be generated at tree level. The calculation is performed in the unbroken phase from the UV poles of gg→H*H, using two independent automated pipelines (FeynRules/FeynArts/FeynCalc/AMFlow+Blade and qgraf/FeynCalc/LiteRed2/FiniteFlow), with an NDR/BMHV scheme check and an agreement statement with independent work [96]. The phenomenological part fits inclusive Higgs signal strengths in both a bottom-up WC fit and top-down vector-like-quark models.","tokens_in":18011,"tokens_out":15654,"duration_ms":138068,"significance":"If correct, Eq. (3.1) completes an important block of the two-loop SMEFT RGE program for the Higgs-gluon coupling, with direct consequences for consistent Higgs fits. The paper's strengths are substantial: two independent diagram-generation and integration pipelines, an explicit γ5-scheme cross-check via the map of Ref. [80], and a statement of agreement with independent work [96]. The RGE result is not circular: no fitted constants or normalization choices enter the computation. However, the completeness of the diagram basis used for Eq. (3.1) rests on a kinematic cancellation for mixed Yukawa-QCD graphs that is asserted but not demonstrated, and this is the main technical concern.","major_comments":[{"comment":"The exclusion of all two-loop diagrams with both external Higgs legs attached to the O_Ht vertex is load-bearing: it reduces the class-7 set to the 24 diagrams that produce Eq. (3.1). The text explicitly cross-checks the cancellation only for the pure-QCD case, i.e. a gluon-propagator correction between the two QCD vertices (Fig. 1b). For the mixed Yukawa-QCD case (Fig. 1c), where an internal Higgs propagator and chiral projectors are present, the remaining amplitude is not shown to be symmetric under p1↔p2; the effective vertex connects H and H*, which are distinct legs, and the Yukawa vertex introduces a preferred fermion direction. Please provide either an explicit two-loop computation of the Fig. 1c family or a rigorous symmetry proof. As written, the completeness of Eq. (3.1) is not fully established, and the stronger 'all loop orders' claim of footnote 2 inherits the same gap.","section":"Sec. 3, Fig. 1c and footnote 2"},{"comment":"Footnote 4 states that the coefficient 3/2 multiplying the O_tH/O_bH terms in Eq. (3.1) differs from the published result of Ref. [27] by an extra 1/2 and that Ref. [27] 'will be updated'. Since Eq. (3.1) is presented as the complete final RGE, the reader cannot reproduce this term from the cited literature as it stands. Please provide the derivation of this coefficient in the present paper or attach the update/erratum to Ref. [27] before publication.","section":"Eq. (3.1), footnote 4"}],"minor_comments":[{"comment":"There is a stray 'h' immediately after the bracket in the displayed equation: 'g_s^2/(16π^2)^2 h +Yb...' appears to be a typographical artifact.","section":"Eq. (3.1)"},{"comment":"The text states that 'the leading divergence is of O(1/ϵ)' to justify the γ5-scheme comparison; it would be useful to state explicitly whether this is the leading 1/ϵ^2 behavior or only the 1/ϵ pole relevant to the RGE, since two-loop poles can have different scheme dependence.","section":"Sec. 3"},{"comment":"The phenomenological comparison is made only against single-operator or paired-operator fits with inclusive Higgs data. A sentence clarifying that no systematic uncertainties from the Higgs signal-strength covariance matrix are included would help the reader judge the strength of the quantitative claims.","section":"Sec. 4.2"},{"comment":"The agreement claim with Ref. [96] refers to a manuscript 'in preparation'; if possible, give more details of the cross-checked terms or make the comparison available as an ancillary file.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The central RGE computation appears technically sound and the two independent pipelines are convincing, but the missing verification of the mixed Yukawa-QCD kinematic cancellation is a genuine completeness gap in the central claim. The discrepancy with Ref. [27] noted in footnote 4 also needs to be resolved before the paper can be used as a definitive reference. These are fixable within the manuscript's scope, hence major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper completes a real gap: the two-loop g_s^2 Y_t^2 (and Y_b) running of C_HG in SMEFT from class-3 and class-7 operators. The first two lines of Eq. (3.1) are genuinely new, and the rest of the result assembles the previously known four-quark and Yukawa-like contributions into one consistent formula. That's what the field has been waiting for, and the authors are not overselling it.\n\nWhat's good: two fully independent computational pipelines (FeynRules/FeynArts/FeynCalc/AMFlow+Blade and qgraf/FeynCalc/LiteRed2/FiniteFlow), an explicit NDR-BMHV map check, and agreement with a parallel unpublished calculation by Born, Fuentes-Martin, and Thomsen. That is exactly the kind of cross-check that makes a high-loop RGE result believable. The γ5 scheme dependence is confined to the four-top term and given in closed form. Credit where due: this is careful, reproducible-in-principle work.\n\nThe soft spots are proportionate. Footnote 4 is the one that actually matters: the contribution from O_tH and O_bH in Eq. (3.1) differs by a factor 1/2 from what the same group published in Ref. [27]. They say Ref. [27] \"will be updated,\" which is honest, but until that update appears, anyone combining this paper with the published literature gets an inconsistency. That needs to be resolved before I would use the formula in a fit.\n\nThe stress-test worry about the kinematic cancellation for mixed Yukawa-QCD diagrams (Fig. 1c) I think does not survive contact with the paper. The two external Higgs legs attach to the same effective vertex, so their momenta enter the rest of the diagram only through p1+p2; the (p1-p2) factor is antisymmetric, and the remainder is symmetric under p1↔p2 regardless of internal Yukawa or chiral insertions. The pure-QCD check was a sanity check, not the only support. Still, an explicit comment or a one-line check for Fig. 1c would be cheap and would shut the loophole for a cautious referee.\n\nMinor but real: the modified RGESolver is not shipped, so the phenomenological section is not reproducible from the text. The fits are illustrative rather than the main point, but if the authors want the two-loop RGEs to be adopted into global fits, the code should be available.\n\nBottom line: this is a serious technical result from a group that knows this machinery. It deserves a serious referee, not a desk rejection. I would ask for: (1) a v2 that either updates Ref. [27] or explains the factor 1/2 in place, (2) a sentence about the mixed-diagram cancellation, and (3) optionally a link to the fit code. After that, I'd cite it.","headline":"Solid, likely-correct completion of a real gap in the two-loop SMEFT RGE program, but the unflagged-by-choice discrepancy with the authors' own earlier paper and the missing fit code make this 'accept after minor revision' rather than 'ready to use.'","tokens_in":18535,"tokens_out":8850,"would_cite":true,"duration_ms":79801,"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":"This paper derives the previously missing two-loop contributions to the renormalization group running of the Higgs-gluon coupling in the Standard Model Effective Field Theory, completing the two-loop Yukawa-induced program for tree-level ge","keywords":["SMEFT","two-loop RGE","Higgs-gluon coupling","Yukawa-induced running","Warsaw basis class 3","Warsaw basis class 7","vector-like quarks","Higgs data fits"],"falsifier":"Compute explicitly the two-loop s-channel triangle diagrams with a single O_Ht insertion and a QCD correction, including the diagram with one Yukawa and one QCD vertex (Fig. 1c), and check whether the sum vanishes; alternatively, compare Eq. (3.1) with the independent two-loop running computation that the authors note is in preparation once it appears, since the paper reports agreement with it.","tokens_in":17572,"feed_emoji":"⚛️","tokens_out":6789,"duration_ms":56017,"temperature":0.7,"pith_summary":"The paper completes the missing piece of the two-loop renormalization group running of the effective Higgs-gluon coupling in the Standard Model Effective Field Theory. It presents new contributions from the D^2 H^4 and D H^2 ψ^2 operator classes (Warsaw basis classes 3 and 7), which are generated at tree level in weakly coupled UV completions, joining previously known four-quark and Yukawa-like operator contributions. The result matters because the Higgs-gluon operator enters gluon-fusion Higgs production at tree level in the SMEFT while the SM contribution is loop-induced, so a consistent loop counting requires including the two-loop running from these tree-level generated operators. The authors also fit to Higgs data and find that two-loop running can sizably tighten bounds on some class 7 operators, though the effect is diluted in vector-like quark models where one-loop matching generates many additional operators.","feed_headline":"Two-loop Yukawa running of the Higgs-gluon coupling completed","feed_subtitle":"Fits to Higgs data show the new running can tighten bounds on third-generation quark operators.","key_machinery":"The kinematic cancellation argument: for a single insertion of a class 7 operator (e.g., O_Ht), the s-channel triangle diagrams contributing to gg→H*H contain a scalar current that contracts with (p1-p2), the difference of the outgoing Higgs momenta, making the diagrams vanish. This justifies discarding all two-loop diagrams in which both external Higgs doublets attach to the effective operator vertex, leaving only diagrams with one external and one internal Higgs leg. The paper also relies on two independent automated computation pipelines based on dimensional regularization and extraction of 1/ε poles to obtain the anomalous dimension, and on the evolution-matrix formalism to convert high-","core_discovery":"This paper computes the two-loop renormalization group equation for the SMEFT operator O_HG = (H†H) G^A_{μν} G^{A,μν} at order g_s^2/(16π^2)^2, presenting contributions from the class 7 operators O_HQ^(1), O_HQ^(3), O_Ht, O_Hb, O_Htb and the class 3 operators O_H□, O_HD. These contributions complete the two-loop Yukawa-induced running proportional to the third-generation Yukawa couplings for potentially tree-level generated operators. The computation exploits a kinematic cancellation: s-channel triangle diagrams with a single class 7 insertion vanish because the scalar current contracts with (p1-p2), so all diagrams where both external Higgs doublets attach to the effective operator vertex a","pith_inferences":["If the kinematic cancellation is generic, it suggests that class 7 operators mix into C_HG only through diagrams where one Higgs doublet is internal; this could be used to organize higher-loop calculations for similar operators, e.g., in di-Higgs production.","The scheme independence of the new terms hints that the γ5 scheme sensitivity in two-loop SMEFT RGEs is confined to specific operator classes (like four-top), which could motivate scheme conventions in future automated two-loop RGE codes.","The sizable tightening of the C_HQ^(3) bound implies that fits which omit two-loop running may underestimate the reach of Higgs data on third-generation quark-Higgs couplings; including top-quark and electroweak precision observables could amplify this effect.","A direct extension would be computing the corresponding two-loop contributions to O_HW, O_HB, and O_HWB; if the pattern persists, the numerical impact on h→γγ and h→Zγ may be smaller than in the gluon case, as the authors expect from the W-loop dominance in the SM."],"forward_implications":["Equation (3.1) completes the two-loop Yukawa-induced RGE for C_HG from potentially tree-level generated operators, so global SMEFT analyses can consistently include these running effects for gluon-fusion Higgs production.","In one-parameter fits to inclusive Higgs data, two-loop running tightens the 2σ bound on C_HQ^(3) sizably, while bounds on class 3 operators C_H□ and C_HD barely change because they enter observables directly.","The bound on the top-bottom operator C_Htb becomes looser at two-loop level, indicating cancellations with one-loop running contributions.","For UV models with vector-like quarks, the inclusion of one-loop matching to O_HG, O_HW, O_HB, and O_HWB reduces the impact of the two-loop running on the fitted parameter regions.","The new contributions are independent of the γ5 scheme, confirming that the scheme dependence in the two-loop RGE of C_HG resides only in the four-top operator contribution."],"fun_headline_variants":["Two-loop Higgs-gluon running in SMEFT now fully computed","New two-loop SMEFT corrections tighten Higgs data bounds","Completing the two-loop Yukawa running of Higgs-gluon coupling","Full two-loop SMEFT running for Higgs-gluon coupling","Two-loop Yukawa running closes SMEFT Higgs-gluon gap"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The paper relies on the claim that all two-loop diagrams in which both external Higgs doublets attach to the effective class-7 vertex vanish identically because the scalar current contracts with (p1-p2); if any mixed Yukawa-QCD diagram of this type survives, the retained 24 diagrams would be incomplete and Eq. (3.1) would miss contributions.","fun_headline_variants_meta":{"raw":{"variants":["Two-loop Higgs-gluon running in SMEFT now fully computed","New two-loop SMEFT corrections tighten Higgs data bounds","Completing the two-loop Yukawa running of Higgs-gluon coupling","Full two-loop SMEFT running for Higgs-gluon coupling","Two-loop Yukawa running closes SMEFT Higgs-gluon gap"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000204,"raw_usage":{"total_tokens":1175,"prompt_tokens":643,"completion_tokens":532,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":387,"completion_tokens_details":{"reasoning_tokens":443}},"tokens_in":387,"tokens_out":532,"duration_ms":4756,"temperature":1.0,"reasoning_tokens":443,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T09:31:21.843624+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute explicitly the two-loop s-channel triangle diagrams with a single O_Ht insertion and a QCD correction, including the diagram with one Yukawa and one QCD vertex (Fig. 1c), and check whether the sum vanishes; alternatively, compare Eq. (3.1) with the independent two-loop running computation that the authors note is in preparation once it appears, since the paper reports agreement with it.","supporting_citations":[],"review_version":1}