{"id":"0bdf12e3-e485-47f1-8c8d-05195337ba94","arxiv_id":"2502.02228","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors computed the real corrections to the NLO Higgs impact factor with finite top mass, confirming the BFKL rapidity-divergence structure and the infinite-top-mass limit.","lead":"This paper reports real-emission corrections to the next-to-leading-order impact factor for forward Higgs production in the BFKL framework, keeping full top-quark mass dependence. It confirms the expected rapidity divergence and its counterterm subtraction, and it reproduces the known infinite-top-mass limit. The full derivation is deferred to the authors' earlier JHEP paper.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claim that the box-like NLO diagrams are fully captured by the FT/FL form factors is unverified; if additional tensor structures survive, Eq. (2)'s rapidity pole and the finite-mt result would be incorrect.","rationale":"The paper is a conference proceedings that delegates the actual computation to the companion JHEP article, Ref. [10]. In that genre, some reliance on the parent paper is normal, and the consistency checks advertised (rapidity divergence, counterterm subtraction, infinite-top-mass limit) are the appropriate checks for this calculation. I found no internal arithmetic contradiction in the formulas shown. However, the load-bearing bridge between the abstract's claim and the result is the statement that the box-like diagrams are captured by the FT/FL form factors of Ref. [10]. That bridge is exactly where the calculation could silently fail: a one-loop 2->3 amplitude with a massive top quark has a tensor structure substantially richer than the two-form-factor vertex of the Born process, and the proceedings text offers no argument that the extra structures vanish after the BFKL projection. The reader's weakest_assumption pointed to the form-factor parametrization; I agree with that identification and sharpen it to the box diagrams and the rapidity-pole coefficient of Eq. (2). Because the proceedings cannot be checked without Ref. [10], the appropriate posture remains CONDITIONAL: acceptance of the central claim is conditional on the form-factor completeness being verified in the parent paper. My concrete test would settle the concern; absent that verification, no change to the reader's verdict is warranted. I also note that the paper commits no obvious error in the portions it does display, and the lack of self-contained derivation is a genre convention rather than evidence of incorrectness.","tokens_in":4486,"tokens_out":11519,"duration_ms":119978,"concrete_test":"Take the six box contributions from Ref. [10] (or recompute them with finite top mass) and contract the resulting one-loop amplitude with the BFKL impact-factor projector used in that reference. Expand the projected scalar in the limit zH->1 with (q-pH) held fixed and nonzero, and check whether the coefficient of 1/(1-zH) is exactly g^2 N |FT(0,-pH^2,mH^2)|^2 q^2/((q-pH)^2)/(4(1-epsilon)(2*pi)^{D-1} sqrt(N^2-1)), with no residual dependence on FL or additional form factors. If residual terms survive the projection, the FT/FL parametrization is incomplete and the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that all real-emission contributions for the gluon-initiated channel, including the six box-like diagrams in which the extra gluon couples to the top-quark loop (Section 3.2, Fig. 2), are expressed in terms of the transverse and longitudinal form factors FT and FL imported from Ref. [10]. This is a nontrivial reduction: for the one-loop amplitude g(q1)+g(q2)->H+pH+g(pg), the extra gluon momentum enters the loop integral, so the amplitude generically has more Lorentz structures than the two-form-factor decomposition of the g*g*H vertex. The paper states 'The boxes have also been expressed in Ref. [10] in terms of certain form factors' but gives neither the decomposition nor the projector that would make the additional rank-3 structures vanish. The only explicit NLO formula, Eq. (2), places the entire rapidity-divergent coefficient into |FT|^2; if any box contribution survives that does not factor through FT, the pole coefficient and the BFKL counterterm cancellation claimed in Section 3.2 would change. The abstract's assertion of 'full dependence on the top-quark mass' therefore rests on an unverified modeling premise, not on a demonstrated internal consistency check.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports the computation of the real corrections to the next-to-leading-order (NLO) Higgs impact factor in the BFKL framework, retaining the full top-quark mass dependence. The authors state that the results reproduce the expected rapidity divergence, that this divergence can be subtracted by a BFKL counterterm, and that the infinite-top-mass limit matches previously known results. The manuscript presents the leading-order impact factor formula, a qualitative discussion of the NLO real-emission contributions (triangular-like and box-like diagrams), and one explicit NLO formula valid in the z_H → 1 limit. The detailed derivations, including the reduction of box diagrams to transverse and longitudinal form factors F_T and F_L, are delegated to the authors' preceding paper, Ref. [10]. The virtual corrections are stated to be the subject of future work.","tokens_in":4690,"tokens_out":4243,"duration_ms":41303,"significance":"If the claimed real-emission computation is correct, it constitutes a valuable step toward a complete NLO Higgs impact factor with exact top-mass dependence, relevant for BFKL phenomenology at the LHC. The paper is honest about the missing virtual part and about relying on Ref. [10] for technical details. However, the manuscript as written contains no new derivations, no full finite-m_t real-emission formula, and no explicit comparison with the infinite-mass limit; it is essentially a summary of claims. The value of the paper therefore rests entirely on the credibility of the referenced long work, and the only quantitative result shown here (Eq. (2)) is the divergent limit. Consequently, the standalone scientific contribution of this proceedings-style paper is limited, though the underlying project may be significant.","major_comments":[{"comment":"The central technical premise, that the six box-like diagrams of Fig. 2 are fully captured by the two form factors F_T and F_L introduced in Ref. [10], is not demonstrated in this manuscript. No tensor decomposition, projector, or reduction argument is given. For the one-loop amplitude g(q1)+g(q2) -> H + pg, the extra gluon momentum enters the loop, so the amplitude generically contains more Lorentz structures than those present in the g*g*H vertex parametrized by F_T and F_L. The coefficient of the rapidity pole in Eq. (2) is proportional to |F_T|^2; if any additional box contribution survives the reduction, this pole coefficient and the claimed BFKL counterterm cancellation would change. The authors should either provide the explicit decomposition/projector here or cite the exact equation in Ref. [10] that establishes it, and state any kinematic conditions under which the additional structures vanish.","section":"Section 3.2, Eq. (2)"},{"comment":"The abstract claims 'the computation of real corrections to the impact factor ... preserving the full dependence on the top-quark mass', but the only NLO formula shown in the paper is the z_H -> 1 limit, Eq. (2). The real-emission cross section at generic z_H, which is the actual result being claimed, is not presented. Either include the full real-emission expression (or the defining integrand) in this paper, or clearly state that the paper is a summary of results obtained in Ref. [10] and soften the abstract accordingly. As it stands, the central claim is not verifiable from the manuscript.","section":"Abstract and Section 3.2"},{"comment":"The bullet states that 'a direct cancellation occurs between the real and virtual contributions within the same phase space region' for soft singularities. This is inconsistent with Section 4, which states that the calculation of virtual corrections is a forthcoming publication. Since the virtual corrections have not been computed, the cancellation cannot have been demonstrated. At most, this is an anticipated cancellation. This affects the claim in the abstract that the 'subtraction of this divergence has been demonstrated' — the soft-singularity part of that demonstration is missing.","section":"Section 3.2, soft singularities bullet"},{"comment":"The statement that 'the impact factor remains consistent with its gauge-invariant definition, utilizing the mt -> infinity expansion up to NNLO' is made without any equation or comparison. If this refers to a check against the infinite-mass results of Refs. [11,12,13], the paper should show at least the leading term of the expansion or the difference between the finite-m_t and infinite-m_t results in some explicit limit. As written, this is an unsupported assertion of a consistency check rather than a demonstrated result.","section":"Section 3.2, final paragraph"}],"minor_comments":[{"comment":"The word 'thesemi-hard' in the opening should be 'the semi-hard' (missing space).","section":"Section 1"},{"comment":"The notation for the impact factor is inconsistent between the first and second lines of Eq. (1): the left-hand side has a subscript 'P P' while the right-hand side introduces dΦ_gg without specifying the corresponding subscript; please clarify the intended notation.","section":"Section 2, Eq. (1)"},{"comment":"The arguments of the form factors, e.g. F_T(0, -q⃗^2, m_H^2), are not defined in the text. Please specify the meaning of the first argument (presumably a squared momentum) and the sign convention of the second argument.","section":"Section 3.1"},{"comment":"The regulator s_Λ and the step function θ are introduced without definition; it would help to state explicitly that θ is the Heaviside function and to specify the dimension of s_Λ.","section":"Section 3.2, Eq. (2)"},{"comment":"The relation between Ref. [11] and the present work is not stated. Since Ref. [11] already computes a Higgs impact factor in the infinite-mass limit, clarify whether the present work extends that calculation to finite m_t or whether Ref. [11] is used only as a benchmark.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a proceedings-style summary; most of the technical content is in the authors' own Ref. [10]. The referee report focuses on the standalone paper, but the editor should consider the venue: for a proceedings, the expectation of reproducing derivations is lower. However, the central claim of the abstract goes beyond what the manuscript demonstrates, and one of the benchmark references (Ref. [13]) shares authors with the present work, so the infinite-mass check is not fully independent. A revision that clearly frames the paper as a summary and adds the missing consistency-check plots or formulas would address the main concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nQuick take: this is a conference proceedings summary of a calculation the same group already published in JHEP 12 (2024) 061, Ref. [10]. The actual result — real corrections to the NLO Higgs impact factor with finite top mass — is in [10], not in this document. The proceedings does a fair job of reporting the singularity structure and the checks that were done, but it is not a standalone derivation.\n\nWhat it does well: the classification of collinear, soft, and rapidity singularities is clean; Eq. (2) shows the explicit rapidity-divergent contribution, which is a concrete anchor; and the infinite-top-mass limit check against [11–13] is a legitimate consistency test. The body is honest about delegating the box-diagram reduction to Ref. [10]. It also states plainly that virtual corrections remain unfinished, which is the right level of candor for a proceedings.\n\nSoft spots: the abstract implies the computation is contained here, but the key reduction of the box-like amplitudes to the FT/FL form factors is imported from [10] without derivation. The stress-test worry about additional tensor structures modifying the rapidity pole is a fair question, but it is a question about [10], not about this text. If you want to verify the result, you must read [10]; this proceedings cannot be refereed in isolation. Also, relative to [10], this adds no new content, only presentation.\n\nFor a full journal, this would deserve a desk reject: it is a derivative summary of already-published work. For the proceedings venue, it is acceptable as a record, with the minor suggestion that the abstract should explicitly say the derivation is in [10]. Bring it to a reading group only if you want a short orientation; cite [10], not this.\n\nBest","headline":"A faithful proceedings summary of a JHEP result; the physics lives in Ref. [10], and the cited version is what deserves your attention.","tokens_in":5266,"tokens_out":3427,"would_cite":false,"duration_ms":34762,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Finite top mass now included in NLO Higgs impact factor.","keywords":["Higgs impact factor","BFKL resummation","next-to-leading order","top-quark mass dependence","real corrections","forward Higgs production","rapidity divergence","infinite top mass limit"],"falsifier":"An independent fixed-order computation of the real-emission amplitude with finite top mass should be compared term by term; if the residue of the $1/(1-z_H)$ rapidity pole does not match the coefficient in Eq. (2), the central claim fails. Alternatively, completing the virtual corrections and showing the soft divergences cancel against these real results would close the loop, since the paper predicts that cancellation but does not display it.","tokens_in":4268,"feed_emoji":"⚛️","tokens_out":7620,"duration_ms":70026,"temperature":0.7,"pith_summary":"This paper aims to complete one ingredient of next-to-leading-order (NLO) calculations for forward Higgs production in the high-energy BFKL factorization framework: the real-emission corrections to the Higgs impact factor, computed with the full top-quark mass dependence instead of the usual infinite-mass approximation. The authors find that in the soft and collinear limits the singularities behave as expected, with collinear contributions matching parton-distribution renormalization and soft pieces cancelling against virtual contributions. In the high-rapidity limit the remaining divergence is the $1/(1-z_H)$ pole required by BFKL, and they exhibit the counterterm that subtracts it. Taking $m_t\\to\\infty$ reproduces the previously established infinite-mass result. If correct, this fixes the real part of the NLO impact factor at exact top mass, leaving only the virtual corrections to finish the NLO calculation.","feed_headline":"Real NLO Higgs corrections computed with full top mass","feed_subtitle":"Finite-mass real-emission corrections match the BFKL rapidity pole and reduce to the infinite-mass limit.","key_machinery":"The load-bearing machinery is the vertex parametrization of the off-shell top-quark loop by the form factors $F_T$ and $F_L$, imported from the companion paper. These functions absorb the full $m_t$ dependence of the loop and convert the Higgs-plus-two-gluon vertex into a simpler building block; the longitudinal form factor enters precisely because both gluons attached to the loop are off shell. The real-emission calculation then attaches one additional quark or gluon line to this vertex and integrates over the extra parton's phase space. The proof that the construction works is the set of consistency checks: absence of soft and rapidity divergences after subtraction, collinear behavior matching PDF renormalization, and recovery of the infinite-mass limit.","core_discovery":"The central claim is that the real corrections to the NLO Higgs impact factor, computed with the top-quark loop at finite mass, are correct and consistent with BFKL factorization. The paper derives both the quark-initiated and the gluon-initiated real-emission contributions, using the transverse ($F_T$) and longitudinal ($F_L$) form factors that encode the production of the Higgs by two off-shell gluons through the top-quark loop. It shows that the only unavoidable divergence in the $z_H\\to 1$ limit is the expected rapidity pole, with coefficient involving $|F_T(0,-\\vec p_H^{\\,2},m_H^2)|^2$, and that this pole is removed by a BFKL counterterm. It also verifies that the collinear singularities have the structure expected from initial-state gluon or quark distributions, and that the $m_t\\to\\infty$ limit of the finite-mass expressions reproduces the known result from the infinite-top-mass approximation. The paper takes these checks as evidence that the real sector of the impact factor is ready to be combined with the universal BFKL Green's function.","pith_inferences":["The paper does not quantify how large finite-top-mass effects are; a natural extension would be a numerical study of the real corrections as a function of Higgs transverse momentum relative to $m_t$, where the infinite-mass approximation is expected to break down.","The use of $F_T$ and $F_L$ form factors from the companion calculation suggests the same parametrization will be reused for virtual corrections; consistency of the full amplitude would then be a nontrivial check the upcoming work will have to pass.","The same form-factor machinery may apply to bottom-quark loop contributions to Higgs production, since the mass dependence is carried exactly; this would extend the result to a second heavy-quark channel.","Extending the one-loop gluon Reggeization check to this impact factor would follow if the announced virtual calculation succeeds, since the paper cites the one-loop result as the motivation for that check."],"forward_implications":["The real part of the NLO Higgs impact factor is now available at finite top mass, so the remaining work to reach a complete NLO impact factor is the virtual corrections, which the paper states are in preparation.","Forward Higgs production at high-energy colliders can be resummed at next-to-leading logarithmic accuracy once the virtual corrections are included, giving predictions in a kinematic region where large energy logarithms dominate.","The check that the infinite-top-mass limit reproduces earlier results means previous calculations using the effective Higgs-gluon coupling remain valid as a limiting case.","The structure of the collinear singularities shows the real corrections are compatible with standard PDF renormalization, so no new non-perturbative input is needed for the real sector.","The rapidity counterterm subtraction demonstrates that the impact factor is compatible with the BFKL scheme, allowing it to be combined with the universal Green's function."],"supporting_citations":[{"why":"Supplies the $F_T$ and $F_L$ form factors for off-shell gluons on which the NLO real corrections are built.","marker":"[10]"},{"why":"Provides an infinite-top-mass NLO impact factor result that the finite-mass calculation must reproduce in the $m_t\\to\\infty$ limit.","marker":"[11]"},{"why":"Another infinite-top-mass NLO impact factor calculation used as a benchmark for the limit check.","marker":"[12]"},{"why":"Earlier computation of the Higgs impact factor in the infinite-top-mass approximation that this work extends.","marker":"[13]"},{"why":"Establishes the one-loop gluon Reggeization with the effective Higgs-gluon coupling, the property the eventual virtual corrections should verify to all orders.","marker":"[17]"}],"fun_headline_variants":["Full top mass NLO real corrections to Higgs impact factor","Finite top mass real NLO Higgs corrections verified","Real NLO Higgs corrections with full top mass now done","BFKL-consistent real NLO Higgs impact factor with top mass","Full top mass real NLO Higgs corrections pass checks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the functions imported from the companion paper completely describe how two off-shell gluons turn into a Higgs through the top-quark loop; if those functions leave out any contribution, the real corrections and all their consistency checks would be affected.","fun_headline_variants_meta":{"raw":{"variants":["Full top mass NLO real corrections to Higgs impact factor","Finite top mass real NLO Higgs corrections verified","Real NLO Higgs corrections with full top mass now done","BFKL-consistent real NLO Higgs impact factor with top mass","Full top mass real NLO Higgs corrections pass checks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000832,"raw_usage":{"total_tokens":3577,"prompt_tokens":833,"completion_tokens":2744,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":449,"completion_tokens_details":{"reasoning_tokens":2673}},"tokens_in":449,"tokens_out":2744,"duration_ms":18268,"temperature":1.0,"reasoning_tokens":2673,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T12:54:24.095881+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An independent fixed-order computation of the real-emission amplitude with finite top mass should be compared term by term; if the residue of the $1/(1-z_H)$ rapidity pole does not match the coefficient in Eq. (2), the central claim fails. Alternatively, completing the virtual corrections and showing the soft divergences cancel against these real results would close the loop, since the paper predicts that cancellation but does not display it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides an infinite-top-mass NLO impact factor result that the finite-mass calculation must reproduce in the $m_t\\to\\infty$ limit."},{"cited_title":"On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling","cited_arxiv_id":"2401.17843","evidence_quote":"Establishes the one-loop gluon Reggeization with the effective Higgs-gluon coupling, the property the eventual virtual corrections should verify to all orders."}],"review_version":1}