{"id":"5e8aa497-ce8d-4c9c-88bf-ba68ec4b9a00","arxiv_id":"2411.12798","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A numerical on-shell matching algorithm uses rational kinematics to compute EFT Wilson coefficients directly in a physical basis, including evanescent shifts.","lead":"This paper presents a numerical method for matching heavy new-physics models onto effective field theories directly in a physical operator basis, bypassing the tedious reduction of redundant Green's bases. It evaluates Feynman amplitudes at exactly chosen rational on-shell momenta, so non-local cancellations happen automatically and results remain exact.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Evanescent-shift prescription in Eq. (7) is justified only by example; a general d-dimensional-then-4d consistency check on an independent operator class would settle whether the claimed scheme is well defined.","rationale":"The reader's weakest_assumption is that the evanescent shift is correctly captured by Eq. (7)'s UV-pole extraction, validated only by the Section 3.4 example. That is exactly the load-bearing spot for the strongest claim (one-loop finite matching, including evanescent shifts, directly in a physical basis). The paper is honest about the scheme dependence ('Of course that does not mean that we are not using a particular evanescent scheme'), and it pins the scheme to NDR plus a reading-point prescription plus the fermion-bilinear basis of [42]. But it does not establish that the numerical d=4 matching plus the soft-region UV-pole correction reproduces that scheme for arbitrary operator structures. The worked example is a single Fierz-type evanescent operator; the mismatch in Eq. (63) shows sensitivity to the order of operations, which makes the absence of a general proof more acute. The internal logic and the cross-checks (Matchete, MatchMakerEFT, [42]) are real evidence, and the tree-level reduction examples and the anomalous-dimension consistency check are independent support, so a rejection would be unwarranted. However, the finite-matching claim is the headline novelty, and its evanescent mechanism is the least-secure link. A second independent check would either confirm the prescription or reveal a scheme/process dependence. The reader's conditional verdict with moderate confidence is appropriate; I agree with their identification of the weakest assumption and see no reason to move to ACCEPT or REJECT without that check.","tokens_in":24363,"tokens_out":1661,"duration_ms":16567,"concrete_test":"Reproduce the Section 3.4 matching for a second independent model, e.g. a heavy real scalar coupled to fermions as y phi psibar psi, matching onto dimension-6 four-fermion and Yukawa-type operators, computing the one-loop finite terms by: (a) the paper's Eq. (7) UV-pole prescription with d-dimensional Dirac algebra; (b) a conventional d-dimensional on-shell matching with explicit evanescent operators as in [42]; (c) an alternative NDR gamma5 reading-point choice. If (a) differs from (b), or if (a) depends on the gamma5/reading-point scheme, Eq. (9) is not a well-defined general procedure.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on Eq. (9), whose evanescent handling via Eq. (7) prescribes: expand in the soft region, extract only the UV pole of each tensor integral (setting scaleless integrals to 1/epsilon_UV with the d-dependence of the integral measure already reduced to 4), then perform all remaining Dirac algebra in d dimensions before taking epsilon to 0. The paper's only genuine validation is the single heavy-Higgs example in Section 3.4, cross-checked against [42]. That example involves a simple 4-fermion Fierz identity where the d-dimensional soft-region difference is unambiguous. The prescription is not proven to be scheme-independent or process-independent: no general argument shows that the 'UV-pole with d=4 measure' replacement commutes with the method of regions, with tensor reduction, or with different gamma5/reading-point prescriptions, or that the resulting finite shift equals the difference of d-dimensional renormalized amplitudes. A second independent operator class, e.g. one involving both chiral and tensor structures or a different internal heavy particle, could expose a scheme mismatch. The SMEFT dimension-8 results in Section 3.2 are delegated to a GitHub notebook and so do not bolster this point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a numerical on-shell matching algorithm for effective field theories. The key idea is to evaluate renormalized physical amplitudes for rational on-shell kinematic configurations, thereby avoiding the analytic cancellation of non-local light-bridge contributions. For one-loop matching, Eq. (9) combines the hard-region contribution of the full theory with the UV-pole parts of the soft-region amplitudes in the full and effective theories; the difference of the latter is claimed to reproduce evanescent shifts. The method is illustrated by three applications: tree-level reduction of a scalar Green's basis to a physical basis up to dimension 8, reduction of bosonic SMEFT Green's-basis operators at dimension 8, one-loop anomalous dimensions in the SMEFT, and finite one-loop matching in a model with a heavy Higgs-like scalar, with cross-checks against Matchete, MatchMakerEFT, and the evanescent-operator literature.","tokens_in":24745,"tokens_out":13020,"duration_ms":142815,"significance":"If correct, the method is a genuinely useful complement to existing automated matching tools: it avoids Green's bases and field redefinitions, works in a user-chosen physical basis, and the rational-kinematics trick makes the cancellation of non-local terms nearly trivial. The scalar example is cross-checked both against explicit field redefinitions and against Matchete, and the finite matching example is checked against MatchMakerEFT and the published evanescent-shift result; these are concrete strengths. The main weakness is that the evanescent-shift prescription in Eq. (7) is the load-bearing element of the finite-matching claim, and it is validated only by a single heavy-Higgs example involving one Fierz identity. A general proof or an independent operator-class test is needed before the method can be regarded as a general algorithm for finite matching.","major_comments":[{"comment":"The evanescent-shift prescription is not derived. The replacement of scaleless tensor integrals by their UV pole, with d-dependent prefactors evaluated at d=4 before completing the Dirac algebra, is presented as a rule, but no general argument shows that this replacement commutes with tensor reduction, with different gamma5/reading-point prescriptions, or with the method of regions, nor that it equals the difference of the corresponding d-dimensional renormalized amplitudes. This matters because Eq. (9) relies on exactly this difference for finite matching. The only validation is the heavy-Higgs example in Sec. 3.4, which is a simple Fierz identity. I request either a general proof of the prescription or an independent check on a second operator class (for example, one involving both chiral and tensor structures, or a different heavy particle), since the advertised capability of 'finite matching, including evanescent contributions' depends on this point.","section":"Sec. 2.1, Eq. (7)"},{"comment":"The extraction of only the UV pole from scaleless integrals requires a separation of UV and IR poles, but the paper does not justify that evanescent O(epsilon) structures cannot multiply 1/epsilon_IR pieces of massless on-shell integrals and produce additional finite terms in Eq. (9). The statement that the effect 'is not affected by IR poles' is asserted rather than shown. Since the soft-region integrals in the on-shell amplitudes of Sec. 3.4 are scaleless, the 1/epsilon_IR partners are present, and the paper should demonstrate that they either cancel between the full and effective theories or are absent for evanescent insertions; otherwise the 'finite part from UV poles' is not uniquely defined.","section":"Sec. 2.1, Eq. (7)"}],"minor_comments":[{"comment":"In the printed code, the line defining ampPhysBasis uses ampRedBasis on the right-hand side rather than ampPhysBasis; as written, the subsequent equations would be trivial identities. The ancillary file is presumably correct, but the listing should be fixed to avoid confusing readers who reproduce the code from the paper.","section":"Appendix C, In[21]"},{"comment":"The text says that evanescent shifts are 'explicitly shown in red', but the arXiv plain-text rendering and monochrome print do not preserve this distinction. Please add a typographic marker (for example, a superscript or footnote) so that the evanescent contributions are identifiable in all formats.","section":"Sec. 3.4, Eqs. (65)-(74)"},{"comment":"The dimension-8 SMEFT reduction is presented as an extension beyond the state of the art, but the full operator definitions and the extended results are partly delegated to a GitHub notebook. Please give a versioned citation or DOI for the notebook and state explicitly which of the displayed formulas were cross-checked with independent methods; as it stands, the reproducibility of this section depends on external, unversioned material.","section":"Sec. 3.2, Eqs. (24)-(38)"}],"recommendation":"major_revision","confidential_remarks":"The paper is honest and technically careful, and I do not see a reason to doubt the correctness of the worked examples. My recommendation of major revision is driven by the generality gap in the evanescent-shift prescription: the central equation (9) is only as solid as the UV-pole replacement rule in Eq. (7), and the current validation is a single Fierz example. A second independent example or a formal argument would turn a promising demonstration into a convincing general method. I would also encourage the authors to make the Section 3.2 notebook versioned and to fix the Appendix C typo before resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis is a genuinely useful paper. It gives an algorithm for on-shell EFT matching that replaces the painful reduction of Green's bases with a numerical solve over rational kinematics, and it demonstrates on three nontrivial examples that the non-local cancellations happen automatically. The scalar reduction is cross-checked with field redefinitions and Matchete; the anomalous-dimension example reproduces the known off-shell result; and the finite one-loop matching reproduces the evanescent shifts of [42]. The SMEFT dimension-8 reduction of redundant operators in Sec. 3.2 is new and already being used in a follow-up renormalization paper. That is real and worth having.\n\nThe soft spot is exactly where the reader and the stress-test put it: the evanescent-shift prescription in Eq. (7). The paper asks you to take the UV pole of the soft-region integrals with the d-dependence of the measure already set to 4, then do the remaining Dirac algebra in d dimensions. This is delicate, and the only genuine validation is the heavy-Higgs example in Sec. 3.4. The authors do not claim a proof of scheme independence; they explicitly say they follow the scheme of [42]. So the concern is not that the paper is wrong—it is that the generality of the method for arbitrary operator structures is not yet established. One more independent example, say with chirality-flipping or tensor structures, would settle it. I would want that before building on the finite-matching part of the code, but I would not call the paper unsound: the examples are checks against established results, and the prescription is clearly stated.\n\nThe SMEFT dimension-8 results are delegated to a notebook; they matter for the paper's utility but not for its central claim. Minor.\n\nOverall, this deserves a serious referee. It is a real methodological contribution, written plainly, with code and cross-checks. I would ask the referee to press on the evanescent-shift generality and to make the ancillary code easier to run, but I would expect it to survive.\n\nMy recommendation: send it to review. I would cite it if I do EFT matching.","headline":"A genuinely useful on-shell matching algorithm with one real soft spot: the evanescent-shift prescription is validated on a single example and deserves a referee's push before the finite-matching part is taken as general.","tokens_in":25121,"tokens_out":2628,"would_cite":true,"duration_ms":27287,"reading_group":"yes","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 proposes a numerical on-shell matching procedure that computes one-loop Wilson coefficients directly in a physical basis, including evanescent shifts, by solving the matching equations at rational on-shell kinematic points.","keywords":["on-shell matching","effective field theory","SMEFT","evanescent operators","Wilson coefficients","Green's basis reduction","method of regions","rational kinematics"],"falsifier":"Run the numerical on-shell algorithm on a one-loop matching problem with a known evanescent shift, for instance the heavy scalar that generates $R_{\\ell e}$ rather than $O_{\\ell e}$ in Section 3.4, and compare the extracted finite coefficient with the closed-form result; if the $\\epsilon$-pole-times-$\\epsilon$ finite part does not match, the ultraviolet-pole-only soft-region rule is wrong.","tokens_in":24150,"feed_emoji":"⚛️","tokens_out":8106,"duration_ms":73231,"temperature":0.7,"pith_summary":"Matching is the step in which a high-energy \"full\" theory is replaced by an effective field theory: the heavy particles are removed and their effects are encoded in the coefficients of local operators. The standard path computes off-shell Green's functions and then reduces a redundant Green's basis to a physical one, a tedious and error-prone job. This paper claims that the whole reduction can be skipped: compute physical on-shell amplitudes in the full and effective theories at randomly chosen rational kinematic points, and solve the matching condition $\\mathcal{M}^{(0)}_{\\mathrm{EFT}} = \\mathcal{M}^{(1),\\mathrm{hard}}_{\\mathrm{full}} + \\mathcal{M}^{(1),\\mathrm{soft}}_{\\mathrm{full}}\\big|_{\\mathrm{UV}} - \\mathcal{M}^{(1),\\mathrm{soft}}_{\\mathrm{EFT}}\\big|_{\\mathrm{UV}}$ numerically. The non-local terms cancel automatically in the difference, and evanescent shifts come out of the ultraviolet-pole parts of soft-region amplitudes without ever constructing evanescent operators. If correct, this makes EFT matching, renormalization, and basis reduction much easier to automate and apply to arbitrary physical bases.","feed_headline":"Numerical on-shell matching skips redundant operator bases","feed_subtitle":"Rational kinematics make the solution exact; evanescent shifts emerge automatically from the UV-pole difference.","key_machinery":"The carrying object is the on-shell matching equation, Eq. (9), together with the rule for extracting evanescent shifts from ultraviolet poles of soft-region amplitudes, Eq. (7). Rational kinematic configurations, generated in $\\mathbb{Q}$ via spinor-helicity variables, make the amplitudes exactly evaluable numbers, so the cancellation of non-local terms and the solution for the Wilson coefficients are both exact. The ultraviolet-pole extraction replaces scaleless integrals with $1/\\epsilon_{\\mathrm{UV}}$ and keeps the Dirac algebra in $d$ dimensions, treating the tensor integral's $1/d$ factor carefully so that the product of an $\\epsilon$ term with a $1/\\epsilon$ pole is retained.","core_discovery":"The authors' central claim is that one-loop on-shell matching can be performed directly in a physical basis through a numerical solution of the on-shell matching equations. The matching condition, Eq. (9), combines the hard-region contribution of the full theory with the difference of the ultraviolet-pole parts of the soft-region contributions of the full and effective theories; this combination is local and includes the evanescent shifts. Rational on-shell kinematics, generated with spinor-helicity variables, make every amplitude evaluation an exact rational number, so the cancellation of light-bridge non-localities and the solution for Wilson coefficients are exact rather than approximate. The paper demonstrates the procedure on a heavy-Higgs model with leptons, a $Z_2$-symmetric scalar theory to dimension 8, and SMEFT dimension-8 examples, and cross-checks the outputs against existing results.","pith_inferences":["If the procedure scales beyond one loop, the hardest part of two-loop on-shell matching—the analytic cancellation of non-localities between full and effective theories—would also become a numerical routine, though the soft-region ultraviolet-pole extraction would need a two-loop analogue.","The evanescent-shift extraction is scheme-dependent through the choice of Dirac algebra and $\\gamma_5$ treatment; a user working in a different scheme would have to convert the resulting Wilson coefficients rather than take them as scheme-independent.","The rational-kinematics core suggests a natural interface with modern amplitude methods such as spinor-helicity and numerical unitarity, which could make full-model Feynman-diagram generation unnecessary for matching.","Operator classes containing Levi-Civita tensors or other genuinely $d$-dimensional structures are the most likely to expose whether the ultraviolet-pole-only soft-region rule is general; testing those would be a direct extension of the paper's example."],"forward_implications":["Green's basis reductions that previously required field redefinitions and equations of motion can be reproduced by solving on-shell matching equations, for any user-chosen physical basis.","Anomalous dimensions and beta functions can be computed directly in a physical basis, without redundant operators or the background-field method for gauge invariance.","Finite one-loop matching, including evanescent shifts, is obtained automatically because the algorithm never needs to construct the evanescent operators explicitly.","A single high-multiplicity on-shell amplitude can determine many Wilson coefficients at once, reducing the number of amplitudes needed to complete a matching.","The same procedure can translate between arbitrary physical bases and can renormalize any effective Lagrangian directly in terms of physical operators."],"supporting_citations":[{"why":"Georgi's on-shell EFT matching defines the physical-amplitude subtraction that the algorithm automates.","marker":"[39]"},{"why":"Supplies the evanescent-operator scheme and the known one-loop evanescent shifts used to define and validate the paper's soft-region extraction.","marker":"[42]"},{"why":"Provides the soft/hard region decomposition of one-loop amplitudes that underlies the matching condition.","marker":"[43]"},{"why":"Method-of-regions expansion that justifies separating soft and hard contributions and expanding heavy propagators.","marker":"[44]"},{"why":"Supplies the dimension-8 bosonic Green's basis whose reduction the paper demonstrates as an application.","marker":"[47]"},{"why":"Algorithm for generating rational on-shell kinematics that makes the numerical solution exact.","marker":"[54]"},{"why":"Spinor-helicity toolbox used to build numerical spinors and polarizations in four dimensions.","marker":"[55]"},{"why":"Automated off-shell matching tool whose results cross-check the finite one-loop matching outputs.","marker":"[37]"},{"why":"Automated matching tool whose basis-reduction results cross-check the scalar and SMEFT examples.","marker":"[36]"}],"fun_headline_variants":["On-shell matching skips redundant bases via rational kinematics","Numerical on-shell matching is exact and uses only physical bases","Matching EFTs directly in physical basis with rational kinematics","Exact on-shell matching: avoid redundant operators completely"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the finite evanescent shift is correctly captured by the ultraviolet-pole parts of the soft-region amplitudes, with scaleless integrals replaced by $1/\\epsilon_{\\mathrm{UV}}$ and the Dirac algebra done in $d$ dimensions before $\\epsilon \\to 0$; the paper validates this on one example rather than proving it in general.","fun_headline_variants_meta":{"raw":{"variants":["On-shell matching skips redundant bases via rational kinematics","Numerical on-shell matching is exact and uses only physical bases","Matching EFTs directly in physical basis with rational kinematics","Exact on-shell matching: avoid redundant operators completely"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000394,"raw_usage":{"total_tokens":2032,"prompt_tokens":875,"completion_tokens":1157,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":1090}},"tokens_in":491,"tokens_out":1157,"duration_ms":8751,"temperature":1.0,"reasoning_tokens":1090,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:11:32.283246+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the numerical on-shell algorithm on a one-loop matching problem with a known evanescent shift, for instance the heavy scalar that generates $R_{\\ell e}$ rather than $O_{\\ell e}$ in Section 3.4, and compare the extracted finite coefficient with the closed-form result; if the $\\epsilon$-pole-times-$\\epsilon$ finite part does not match, the ultraviolet-pole-only soft-region rule is wrong.","supporting_citations":[{"cited_title":"Georgi, On-shell effective field theory , Nucl","cited_arxiv_id":null,"evidence_quote":"Georgi's on-shell EFT matching defines the physical-amplitude subtraction that the algorithm automates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Spinor-helicity toolbox used to build numerical spinors and polarizations in four dimensions."}],"review_version":1}