{"id":"610efb6c-a40a-497d-8b49-4a05c589fe12","arxiv_id":"2607.04182","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"In the minimal TMC scheme, one-loop nonsinglet quasi-PDFs separate into explicit cutoff (and boundary UV) counterterms plus a remainder that carries the collinear IR pole and finite matching kernel.","lead":"This paper shows how to split one-loop quasi-PDFs into cutoff-dependent counterterms and an IR-safe matching remnant using a transverse-momentum cutoff. The split clarifies scheme dependence before matching to lightcone PDFs and offers a template for other lattice renormalization schemes.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The strongest claim is supported by the explicit one-loop calculation: linear tadpole and ln(Λ²/μ²) wave-function pieces plus boundary poles at x=±∞ are assigned to the TMC counterterm (Eq. 3.43), the remnant keeps the full collinear IR pole and the finite full-line distribution (Eq. 3.46), and the resulting matching kernel matches the MS full-line result of Izubuchi et al. except for the finite local constant expected from the different wave-function finite-term assignment. The only soft spot is that the minimal prescription itself is a definition, not a uniqueness theorem; the paper states this openly and uses it as a benchmark. Because that definitional character does not undermine the internal derivation or the cross-check against the known MS kernel, no load-bearing concern lands and the reader’s ACCEPT verdict stands.","tokens_in":23107,"tokens_out":532,"duration_ms":4349,"concrete_test":"Independently recompute the finite δ(1−x) coefficient in the TMC remnant by combining the endpoint expansion of F(x) in Appendix A.3 with the finite part of the wave-function remnant (Eq. 3.34); confirm that it equals 3/2 ln(μ²/4p_z²)+2 as written in Eq. 3.46 / A.21, and that subtracting the MS light-cone IR pole then reproduces Eq. 3.49. Agreement leaves the claim intact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper’s central claim is a transparent one-loop bookkeeping exercise under an explicitly chosen minimal TMC definition (Sec. 2, Eqs. 2.3–2.7): scheme dependence is identified with the large-k_⊥ asymptotic integrand plus full-line UV boundary poles, while the remainder retains the collinear IR pole and finite matching pieces. That definition is not derived from uniqueness or RG invariance, but the manuscript never claims it is; it presents the choice as a diagnostic benchmark and checks that, after the stated subtraction, the nonlocal full-line matching kernel agrees with Izubuchi et al. (up to the expected finite δ(1−x) wave-function shift). No internal inconsistency, missing cancellation, or algebraic gap appears in the tadpole/sail/vertex/wave-function decomposition or in the distribution conventions of Appendix A. The reader’s weakest_assumption correctly flags a definitional choice rather than a hidden flaw.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper computes the one-loop nonsinglet quark quasi-PDF with a transverse-momentum cutoff (TMC) and organizes the result into a minimal TMC counterterm versus a renormalized remnant. Scheme dependence is identified with the large-k_⊥ asymptotic integrand (linear tadpole Wilson-line term and ln(Λ²/μ²) wave-function piece) plus UV boundary poles of the full-line x-distribution at x=±∞; the remnant retains the collinear IR pole and the finite full-line distribution used for matching to the MS lightcone PDF. After subtraction, the nonlocal matching kernel agrees with the known full-line MS result of Izubuchi et al., up to a finite δ(1−x) shift from the wave-function finite part. The RG anomalous dimension of the TMC quasi-PDF is written as a full-line distribution, separating finite-x and boundary-supported pieces.","tokens_in":23297,"tokens_out":937,"duration_ms":20248,"significance":"If correct, the work supplies a transparent, diagram-by-diagram bookkeeping of how UV/cutoff and IR pieces enter the quasi-PDF before matching, with explicit distribution conventions on the full line (including double-plus and boundary distributions). That organization is a useful diagnostic benchmark for LaMET renormalization discussions, even though TMC itself is not the practical lattice scheme. Strengths include the analytic one-loop separation (tadpole/sail/vertex/wave function), the careful treatment of the linear divergence as a counterterm before matching, the a-posteriori check against the MS full-line kernel, and the clear distinction between finite-x matching evolution and full-line anomalous dimension. The contribution is clarifying rather than transformative, but it is technically solid and of interest to the LaMET/PDF community.","major_comments":[],"minor_comments":[{"comment":"Abstract and Sec. 5: the phrase “provides a benchmark for examining analogous separations in other renormalization schemes” is aspirational; a short sentence noting that RI/MOM or hybrid schemes lack an explicit hard cutoff, so the asymptotic-integrand rule must be rephrased in terms of subtraction conditions, would set expectations without overselling.","section":null},{"comment":"Sec. 2, after Eqs. (2.5)–(2.7): state earlier and more prominently that “minimal” means finite pieces left after the large-k_⊥ asymptotics stay in the renormalized quasi-PDF by definition, and that a different finite-term assignment only reshuffles local δ(1−x) constants (as later shown vs MS).","section":null},{"comment":"Eq. (3.32) and App. A.3: the finite constant “1” in the TMC wave-function renormalization is scheme-specific; a one-line comparison to the pure-DR wave-function structure (1/ε_UV − 1/ε_IR with no finite constant) would help readers see immediately why only the δ(1−x) coefficient differs from Ref. [12].","section":null},{"comment":"Fig. 1 caption: the wave-function diagram is mentioned as “not shown”; either include a fifth panel or drop the remark so the figure stands alone.","section":null},{"comment":"Notation: the same symbol ε is used for IR poles at finite x and UV boundary poles at infinity (with subscripts IR/UV); a brief reminder when 1/ε_UV first appears in Eq. (3.41) that this is a full-line distribution regulator, not a transverse-momentum pole, would reduce confusion.","section":null},{"comment":"Typos/style: “spacetime” vs “space-time” is mixed; “LaMET evidently yields” (p. 2) is slightly informal; check consistency of “TMC,ct” vs “TMC,ren” subscript ordering throughout Sec. 3.","section":null}],"recommendation":"accept","confidential_remarks":"Novelty is modest—essentially a careful reorganization of a known one-loop calculation under an explicitly chosen minimal cutoff prescription—but the distribution-level bookkeeping and the finite-x vs full-line RG distinction are clean and useful. Fit for JHEP is appropriate as a technical clarification paper; I would not demand expansion to RI/MOM in this manuscript."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a careful one-loop theory note that does exactly what the abstract says. Chay takes the old transverse-momentum cutoff regulator, isolates the large-k_perp asymptotics diagram by diagram (tadpole, sail, vertex, wave function), and writes a minimal TMC counterterm that holds the linear Wilson-line piece, the ln(Lambda^2/mu^2) wave-function term, and the full-line UV boundary poles at x=+-infty. What is left is a renormalized remnant that still carries the collinear IR pole and the finite full-line distribution needed for matching. After subtraction the nonlocal pieces of the matching kernel agree with Izubuchi et al., up to the expected finite delta(1-x) shift from how the wave-function constant is assigned. That check is the main evidence the separation is not just cosmetic.\n\nWhat is actually new is the organization, not the regulator itself. The double-plus convention for the linear tadpole, the explicit split of the anomalous dimension into finite-x and boundary pieces, and the two-step subtraction (explicit Lambda first, then boundary poles) are written cleanly and with usable distribution definitions in the appendix. The paper is honest that the \"minimal\" assignment of finite pieces is a definitional choice, not a uniqueness theorem; it presents TMC as a diagnostic benchmark for later schemes rather than a lattice-ready prescription.\n\nSoft spots are minor and proportional. The work is purely one-loop and nonsinglet; there is no lattice data, no higher-order check, and no claim that the same split is automatic in RI/MOM or hybrid schemes. The finite delta(1-x) difference with pure MS is correctly traced to wave-function renormalization and is not hidden. Citation pattern is appropriate (Xiong, Izubuchi, hybrid/ratio literature).\n\nThis is for people who actually write matching kernels or renormalize spatial correlators. It will not change collider PDF usage, but it is a useful reference for scheme bookkeeping inside LaMET. I would send it to referees; the algebra is transparent and the central claim is supported by the derivation as stated. Worth a look if you are in that subfield; otherwise you can skip.","headline":"Clean one-loop bookkeeping of TMC quasi-PDF renormalization: explicit counterterm vs IR-bearing remnant, with a solid check against the known MS full-line kernel.","tokens_in":23912,"tokens_out":547,"would_cite":true,"duration_ms":5491,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A transverse-momentum cutoff cleanly separates scheme-dependent UV pieces of quasi-PDFs from the IR structure needed for matching.","keywords":["quasi-PDF","LaMET","transverse-momentum cutoff","scheme dependence","matching coefficient","full-line distributions","linear divergence","renormalization group"],"falsifier":"Recompute the one-loop matching coefficient after deliberately moving a finite constant from the wave-function remnant into the TMC counterterm and check whether the nonlocal x-dependent kernels still agree with the known full-line MS result while only the coefficient of delta(1-x) shifts.","tokens_in":23942,"feed_emoji":"⚛️","tokens_out":770,"duration_ms":5508,"temperature":0.7,"pith_summary":"Quasi-PDFs are equal-time spatial correlators that lattice QCD can compute; they must be matched perturbatively onto ordinary lightcone parton distributions. The one-loop expressions mix an infrared collinear pole (required for that matching) with ultraviolet, scheme-dependent pieces that depend on how the spatial operator is renormalized. The paper adopts a minimal transverse-momentum-cutoff (TMC) regulator and shows that the scheme-dependent sector is exactly the set of terms that carry explicit cutoff dependence: a linear Wilson-line divergence, a logarithmic wave-function term, and ultraviolet boundary poles that appear when the quasi-PDF is treated as a distribution on the whole real line. Once those terms are subtracted into a counterterm, the remainder retains the full collinear infrared pole plus the finite full-line distribution that enters the matching coefficient. The resulting nonlocal matching kernel agrees with the known full-line MS result up to a finite local constant fixed by the wave-function prescription. The same organization also makes the renormalization-group evolution of the quasi-PDF transparent: finite-x evolution is controlled by the logarithmic counterterm, while the boundary poles complete the anomalous dimension of the full-line distribution. The construction is offered as a transparent benchmark for disentangling scheme dependence in more practical lattice renormalization schemes.","feed_headline":"Cutoff isolates scheme pieces of quasi-PDFs from matching IR","feed_subtitle":"Linear, log, and boundary UV terms go to the counterterm; the collinear pole and finite kernel remain for matching.","key_machinery":"The asymptotic large-k_perp separation of every one-loop integrand (Eqs. 2.3-2.7): the scheme-dependent piece is defined as the integral of the large-k_perp asymptotic form up to the cutoff Lambda, while the convergent remainder is independent of Lambda and carries the IR structure required for matching.","core_discovery":"At one loop in the minimal TMC scheme the bare nonsinglet quark quasi-PDF decomposes as bare = TMC counterterm (explicit Lambda-dependent linear tadpole + ln(Lambda^2/mu^2) wave-function term + full-line UV boundary poles at x=+-infinity) + renormalized remnant that keeps the complete collinear IR pole and the finite full-line distribution needed for matching; after subtraction the nonlocal matching kernel agrees with the MS full-line result up to a finite delta(1-x) shift fixed by the wave-function renormalization.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["TMC scheme splits quasi-PDF scheme dependence from collinear IR","Minimal cutoff isolates scheme sector in one-loop quasi-PDFs","Transverse cutoff decomposes quasi-PDF into scheme and matching terms","Scheme pieces of quasi-PDFs disentangled via TMC at one loop","Cutoff method separates scheme-dependent UV from IR in quasi-PDFs"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The definition of the scheme simply declares that every term without explicit cutoff dependence belongs to the renormalized quasi-PDF; a different assignment of those finite pieces would change the local matching constant and the finite-x anomalous dimension.","fun_headline_variants_meta":{"raw":{"variants":["TMC scheme splits quasi-PDF scheme dependence from collinear IR","Minimal cutoff isolates scheme sector in one-loop quasi-PDFs","Transverse cutoff decomposes quasi-PDF into scheme and matching terms","Scheme pieces of quasi-PDFs disentangled via TMC at one loop","Cutoff method separates scheme-dependent UV from IR in quasi-PDFs"]},"model":"grok-4.5","effort":"low","cost_usd":0.003884,"raw_usage":{"total_tokens":1248,"prompt_tokens":805,"num_sources_used":0,"completion_tokens":77,"cost_in_usd_ticks":38840000,"prompt_tokens_details":{"text_tokens":805,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":366,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":805,"tokens_out":77,"duration_ms":3123,"temperature":1.0,"reasoning_tokens":366,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T21:07:03.882244+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Recompute the one-loop matching coefficient after deliberately moving a finite constant from the wave-function remnant into the TMC counterterm and check whether the nonlocal x-dependent kernels still agree with the known full-line MS result while only the coefficient of delta(1-x) shifts.","supporting_citations":[],"review_version":1}