{"id":"368b90b6-e621-42d1-bea9-33eb80f51efa","arxiv_id":"1909.02619","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Soft-gluon resummation results for single top plus Z/photon production via anomalous FCNC couplings, showing large approximate NNLO K-factors, are presented for LHC energies.","lead":"This paper computes higher-order QCD corrections for producing a top quark with a Z boson or photon through rare flavor-changing interactions, and reports that the corrections boost the predicted rates by 36 to 49 percent at 13 TeV. It is a short conference proceedings that largely summarizes results already published by the same group, useful to experimentalists searching for anomalous top-quark couplings.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"aNNLO K-factors rest on unverified soft-gluon dominance at 13 TeV; only NLO accuracy is validated against complete fixed-order results.","rationale":"The reader's weakest assumption correctly identifies soft-gluon dominance as the load-bearing premise, and my reading does not displace that concern. I do not see an internal inconsistency in the formulas; the issue is an external validation gap at exactly the order relevant to the central claim. The NLO validation cited in Sec. 5 is encouraging but insufficient by itself, because fixed-order logarithms being dominant at one order does not guarantee the same dominance at the next order, especially at 13 TeV where threshold suppression is weaker. The absence of the uncertainty estimates promised in the abstract compounds the problem by leaving no quantitative handle on the size of missing hard terms. These considerations support the reader's conditional verdict without requiring rejection, so the verdict is unchanged.","tokens_in":5682,"tokens_out":5984,"duration_ms":68374,"concrete_test":"Compute the full NLO total cross sections for gu->tZ and gu->tgamma at 13 TeV with the same inputs as the paper (MMHT2014 NNLO PDFs, kappa=0.01, central scales) using the complete NLO results of Refs. [6] and [12], and tabulate them against the aNLO values obtained from Eq. (5). If the fractional difference exceeds the extra increment claimed at aNNLO over aNLO (5% for tgamma, 13% for tZ), the soft approximation is not validated at the precision required by the headline. As a secondary check, recompute the aNNLO K-factors with mu_R and mu_F varied by a factor of two; if the resulting scale band covers more than half of the claimed NNLO increment, the K-factors should be reported with an uncertainty band rather than as single percentages.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline numbers (49% for gu->tZ, 36% for gu->tgamma at 13 TeV) come from Eq. (8), which contains only threshold [ln^k(s4/mt^2)/s4]_+ and delta(s4) terms with no matched hard contribution. The paper's support for the assumption that these terms 'dominate ... the higher-order corrections' is the statement in Sec. 5 that the results 'approximate well [14,15] the complete corrections at NLO [6,12].' That validates aNLO, not aNNLO. At 13 TeV the partonic system is farther from threshold than at 7 or 8 TeV, so hard non-soft NNLO terms could be comparable to the claimed NNLO increment (13% over aNLO for tZ, 5% over aNLO for tgamma). If the uncalculated hard NNLO contribution is a few percent of LO, the quoted K-factors would shift by a comparable amount, directly changing the conversion of LHC cross-section limits into FCNC coupling limits. The abstract's promised uncertainty discussion is not present in the text, so there is no error band that would indicate whether this risk is under control.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies higher-order QCD corrections to single-top production in association with a Z boson or a photon via anomalous FCNC couplings, specifically the partonic processes gq→tZ and gq→tγ. The authors use the soft-gluon resummation formalism developed in their earlier papers to write approximate NLO, NNLO, and NNNLO formulas (Eqs. (5)-(8)), and present numerical total cross sections and differential distributions in top rapidity and transverse momentum at LHC energies of 7, 8, 13, and 14 TeV using MMHT2014 NNLO PDFs. The central numerical results are the K-factors: at 13 TeV, the aNNLO corrections increase the gu→tZ cross section by 49% (versus 36% at aNLO) and the gu→tγ cross section by 36% (versus 31% at aNLO), with much smaller further aNNNLO contributions. The paper argues that these corrections are important for converting LHC cross-section measurements into limits on anomalous couplings κ_tqZ and κ_tqγ.","tokens_in":5882,"tokens_out":8868,"duration_ms":92177,"significance":"If the quoted aNNLO K-factors are reliable, the paper provides practically useful input for ATLAS/CMS searches for top-quark FCNC couplings; corrections of tens of percent change the extracted coupling limits. The calculation has a clean parametric setup: the only free parameters are the two anomalous couplings, which scale the cross sections quadratically, and the results are not fitted to data. The paper also supplies results at several LHC energies and for multiple distributions, which is useful. Its main limitations are that the central formulas are not derived here, the aNNLO accuracy is not validated against a complete NNLO calculation, and no numerical uncertainties are provided despite being announced in the abstract; these limitations must be addressed before the numbers can be used at face value.","major_comments":[{"comment":"The abstract states that the paper will \"discuss uncertainties,\" but the text contains no numerical uncertainty estimate (no scale variation, PDF error, or scheme dependence) for any of the quoted cross sections or K-factors. Because the central claim is that aNNLO corrections change the 13 TeV cross sections by tens of percent, a reader cannot judge whether the 49% and 36% numbers are stable without an uncertainty estimate. At minimum, the authors should give the residual scale dependence at aNLO/aNNLO and, if possible, a PDF uncertainty.","section":"Abstract and Sections 3-4"},{"comment":"The claim that the aNNLO results are trustworthy rests on the assertion in Section 1 that soft-gluon corrections \"dominate (and thus approximate well) the higher-order corrections.\" The only validation cited, in Section 5, is that the approximations reproduce the complete NLO results of Refs. [6,12]; this says nothing about the size of hard non-soft NNLO terms, which are not included in Eq. (8). Since at 13 TeV the partonic system is farther from threshold than at 7 or 8 TeV, the uncalculated hard NNLO terms could be comparable to the additional aNNLO increment beyond aNLO (roughly 10% of the cross section for tZ and 4% for tγ based on the quoted K-factors). Please either compare with a complete NNLO calculation where one exists, or provide a quantitative argument (e.g., power-suppressed corrections or scale variation) that the missing hard terms are small.","section":"Section 1 and Section 5"},{"comment":"Eq. (8) is presented as the aNNLO soft-gluon correction, but unlike Eq. (5) it contains no δ(s4) term. The coefficient of δ(s4) at aNNLO contributes to the total cross section after integration, and the text does not state whether it is zero, omitted for brevity, or beyond the stated NLL accuracy. Please clarify the logarithmic accuracy of Eq. (8) and, if a δ(s4) term exists, display it or cite the specific equation in Ref. [14] or [15] from which it can be obtained.","section":"Eq. (8) and Section 2"}],"minor_comments":[{"comment":"The sentence \"with a 49% increase in the total cross section at 13 TeV at aNNLO compared to the 36% increase at aNLO\" is ambiguous; state explicitly that both numbers are K-factors relative to LO, or give aNNLO/aNLO ratios.","section":"Section 3"},{"comment":"The text never specifies the central renormalization and factorization scales used for the numerical results, nor the values of α_s and m_t used in the plots; please add this information or give a precise pointer to the corresponding paragraphs of Refs. [14,15].","section":"Sections 3-4"},{"comment":"The one-loop soft anomalous dimension is given in Feynman gauge; the gauge choice and the definition of the color basis should be stated to make the formula unambiguous.","section":"Eq. (4)"},{"comment":"Reference [18] contains a typo: \"Molytinski\" should be \"Motylinski.\"","section":"References"},{"comment":"The right insets of Figs. 2 and 5 are labeled only \"1\" and \"2\" on the vertical axis; please use explicit tick labels with the K-factor values.","section":"Figures 2 and 5"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution that relies almost entirely on the authors' previous papers [14,15,17] for the master formulas. That is not improper in itself, but the present manuscript is not self-contained, and the referee report should be read with that context in mind. The main load-bearing issue is the lack of any uncertainty estimate despite the abstract's promise, together with the unvalidated soft-gluon-dominance assumption at aNNLO; these are fixable in revision but should not be left implicit."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a conference proceedings, not a new research paper. The core numbers for gq->tZ and gq->tγ were already published by the same group in [14] and [15]; the update here is MMHT2014 PDFs and a few aNNNLO points, and the paper itself says the earlier CT14 results are very similar. It is a useful compact summary, but it does not stand alone.\n\nCredit where it is due: the soft-gluon formulas are written out explicitly, the figures are clear, and the K-factors (49% for tZ, 36% for tγ at 13 TeV) are exactly what an experimental FCNC search would need to translate cross-section limits into coupling limits. The aNLO results are checked against full NLO from independent groups.\n\nThe weak spots are real. The abstract promises a discussion of uncertainties, and the text contains none—no scale variation, no PDF errors, no bands in the figures. That is a mismatch. The stress-test concern about aNNLO soft-gluon dominance lands: the only validation the authors cite is at NLO (Sec. 5, citing [14,15] against [6,12]). At 13 TeV the partonic system is farther from threshold, so hard non-soft NNLO terms could plausibly be a few percent of LO and shift the quoted aNNLO increment (13% over aNLO for tZ, 5% for tγ) by a non-negligible amount. The formalism is standard and the authors may well be right; the problem is the reader has no way to assess the risk because no uncertainty estimate is shown. Most equations are quoted without derivation, and the text repeatedly defers to [14] and [15] for details, so as a standalone submission there is little new content to referee.\n\nWho is this for? Someone who wants a quick single-reference summary of the group's K-factors with MMHT2014 PDFs, or an experimentalist willing to go to the earlier papers for details. I would not send it out to referees; I would recommend the authors either expand it into a full paper with uncertainty bands and a direct comparison to complete NNLO where available, or publish it as a proceedings note without claiming to discuss uncertainties. For my own work, I would cite [14] and [15] for the actual numbers, not this paper.","headline":"A conference proceedings that repackages the authors' own prior aNLO/aNNLO results with a new PDF set; useful as a quick reference, but it does not stand alone as a new result and its abstract promises uncertainty discussion the text never delivers.","tokens_in":6462,"tokens_out":4128,"would_cite":false,"duration_ms":40051,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that approximate NNLO soft-gluon corrections raise predicted FCNC single-top cross sections by 49% for tZ and 36% for tγ at 13 TeV, so rate limits on anomalous top couplings must be rescaled.","keywords":["soft-gluon corrections","threshold resummation","single top-quark production","tZ production","tgamma production","anomalous FCNC couplings","NNLO approximations","LHC cross sections"],"falsifier":"Compute the complete NNLO QCD corrections for $gu \\to tZ$ and $gu \\to t\\gamma$ and compare them with the aNNLO results presented here; if the full NNLO-over-LO K-factors differ from 1.49 and 1.36 at 13 TeV by more than the quoted scale uncertainties, the threshold-dominance assumption is contradicted.","tokens_in":5449,"feed_emoji":"⚛️","tokens_out":6574,"duration_ms":59536,"temperature":0.7,"pith_summary":"This paper calculates higher-order soft-gluon radiative corrections to single top-quark production in association with a Z boson or a photon, driven by anomalous flavor-changing neutral-current (FCNC) couplings. It presents total cross sections and differential distributions for the partonic processes $gq \\to tZ$ and $gq \\to t\\gamma$ at LHC energies, using approximate NLO, NNLO, and NNNLO (aNLO, aNNLO, aNNNLO) results. The central numerical finding is that the aNNLO corrections enlarge the 13 TeV total cross section by 49% for $gu \\to tZ$ and 36% for $gu \\to t\\gamma$ relative to leading order, with aNNNLO adding only a small amount. These K-factors matter because experimental searches for anomalous top couplings convert measured rate limits into coupling limits, and neglecting the corrections would bias those bounds.","feed_headline":"Soft-gluon corrections boost single-top tZ and tγ rates up to 49%","feed_subtitle":"New K-factors at approximate NNLO change the conversion of LHC limits on anomalous top couplings.","key_machinery":"The central object is the soft anomalous dimension $\\Gamma_S$ for the partonic process $g q \\to t A$, which controls the exponentiation of soft-gluon logarithms near partonic threshold, where the extra energy $s_4 = s + t + u - m_t^2 - m_A^2$ goes to zero. The cross section is built from master formulas (Eqs. (5)-(8)) that express the aNLO and aNNLO corrections as $F^{LO}$ times plus-distributions $[\\ln^k(s_4/m_t^2)/s_4]_+$, with coefficients $c_3, c_2, c_1$ determined by the color factors $C_F$, $C_A$, the kinematics, and the factorization/renormalization scales. These formulas turn the soft anomalous dimension into final cross sections and distributions after convolution with PDFs.","core_discovery":"The paper claims that soft-gluon (threshold) logarithms dominate the higher-order QCD corrections for $gq \\to tZ$ and $gq \\to t\\gamma$, so that the approximate corrections built from those logarithms stand in for the complete corrections. Using this approximation, it finds that the aNNLO corrections are large at all LHC energies: for $gu \\to tZ$ at 13 TeV the cross section grows by 49% over LO (with aNLO giving 36%), and for $gu \\to t\\gamma$ at 13 TeV by 36% over LO (with aNLO giving 31%). The aNNNLO corrections are much smaller, suggesting the series has essentially converged. Rapidity and transverse-momentum distributions receive similarly significant enhancements, so the higher-order effects matter for both inclusive and differential measurements.","pith_inferences":["Inference: If the soft-gluon dominance assumption holds, a future complete NNLO computation for these processes should land close to the quoted aNNLO K-factors; any sizeable deviation would signal that hard non-threshold radiation is important.","Inference: The same threshold-logarithm machinery could be carried over to other single-top FCNC final states, such as $tH$, where soft corrections may be comparably large.","Inference: The K-factors being larger than unity implies that experimental collaborations' existing LO-based limits are numerically over-optimistic, so reinterpreting published limits with these corrections is a direct and testable application.","Inference: Differential measurements of the top-quark $p_T$ tail could discriminate between LO and aNNLO shapes, providing a data-driven check of the threshold approximation."],"forward_implications":["Searches for anomalous $tqZ$ and $tq\\gamma$ couplings at the LHC should use the aNNLO K-factors (1.49 for $tZ$, 1.36 for $t\\gamma$ at 13 TeV) rather than LO cross sections when interpreting limits, otherwise the derived bounds on $\\kappa_{tqZ}$ and $\\kappa_{tq\\gamma}$ would be too tight.","Because the predicted cross section increases, current exclusion limits on FCNC couplings become weaker once these corrections are included.","The differential $p_T$ and rapidity distributions also change shape with the higher-order corrections, so experimental analyses using kinematic distributions need corrected predictions, not just a flat K-factor.","The small aNNNLO increment indicates the soft-gluon series is under control, giving confidence that the aNNLO numbers are a stable target for the full NNLO prediction."],"supporting_citations":[{"why":"Provides the aNLO and aNNLO soft-gluon formulas and earlier numerical results for $gq \\to tZ$ that this paper extends.","marker":"[14]"},{"why":"Provides the analogous soft-gluon corrections for $gq \\to t\\gamma$, the foundation for the tγ numbers here.","marker":"[15]"},{"why":"Full NLO calculation cited as the complete-correction benchmark for the soft-gluon approximation.","marker":"[6]"},{"why":"Full NLO calculation cited as another benchmark that the soft-gluon approximations reproduce.","marker":"[12]"},{"why":"MMHT2014 NNLO parton distribution functions used for all numerical cross sections and distributions.","marker":"[18]"}],"fun_headline_variants":["Soft-gluon effects raise tZ and tγ cross sections by up to 49%","Higher-order QCD adds up to 49% to single-top Z and photon production","Soft-gluon logarithms add up to 49% to single-top tZ and tγ rates","aNNLO soft-gluon corrections enhance tZ and tγ production by up to 49%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that soft-gluon (threshold) logarithms dominate the full QCD corrections, so the 'approximate' NNLO result is close to the complete NNLO result.","fun_headline_variants_meta":{"raw":{"variants":["Soft-gluon effects raise tZ and tγ cross sections by up to 49%","Higher-order QCD adds up to 49% to single-top Z and photon production","Soft-gluon logarithms add up to 49% to single-top tZ and tγ rates","aNNLO soft-gluon corrections enhance tZ and tγ production by up to 49%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001256,"raw_usage":{"total_tokens":5069,"prompt_tokens":788,"completion_tokens":4281,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":404,"completion_tokens_details":{"reasoning_tokens":4180}},"tokens_in":404,"tokens_out":4281,"duration_ms":34698,"temperature":1.0,"reasoning_tokens":4180,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:44:31.364193+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the complete NNLO QCD corrections for $gu \\to tZ$ and $gu \\to t\\gamma$ and compare them with the aNNLO results presented here; if the full NNLO-over-LO K-factors differ from 1.49 and 1.36 at 13 TeV by more than the quoted scale uncertainties, the threshold-dominance assumption is contradicted.","supporting_citations":[{"cited_title":"Higher-order corrections for $tZ$ production via anomalous couplings","cited_arxiv_id":"1712.01144","evidence_quote":"Provides the aNLO and aNNLO soft-gluon formulas and earlier numerical results for $gq \\to tZ$ that this paper extends."},{"cited_title":"Associated production of a top quark with a photon via anomalous couplings","cited_arxiv_id":"1808.09014","evidence_quote":"Provides the analogous soft-gluon corrections for $gq \\to t\\gamma$, the foundation for the tγ numbers here."},{"cited_title":"Next-to-leading order QCD corrections to the top quark associated with $\\gamma$ production via model-independent flavor-changing neutral-current couplings at hadron colliders","cited_arxiv_id":"1101.5346","evidence_quote":"Full NLO calculation cited as the complete-correction benchmark for the soft-gluon approximation."},{"cited_title":"Next-to-leading order QCD corrections to $tZ$ associated production via the flavor-changing neutral-current couplings at hadron colliders","cited_arxiv_id":"1103.5122","evidence_quote":"Full NLO calculation cited as another benchmark that the soft-gluon approximations reproduce."}],"review_version":1}