{"id":"095978e6-f4e8-4f63-ac08-bf1cee9c66c5","arxiv_id":"2605.17389","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":3.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"Light-cone quark model PDFs for kaon and heavy mesons are evolved via NLO DGLAP to predict EIC structure functions and COMPASS Drell-Yan cross sections while showing heavy constituents dominate momentum fractions.","lead":"This paper computes parton distribution functions for the kaon and heavy pseudoscalar mesons in a light-cone quark model, evolves them with NLO DGLAP equations, and generates predictions for structure functions and Drell-Yan cross sections at future experiments. A smart generalist might read it for insight into how heavy quark contributions are modeled for upcoming collider measurements.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Initial-scale PDFs from light-cone quark model correlation functions may not reliably capture momentum distributions in heavy mesons","rationale":"The reader's weakest assumption matches the load-bearing step exactly: the dominance demonstration is a direct numerical output of the initial PDFs. No additional internal inconsistency (e.g., in the DGLAP implementation or sum-rule checks) is visible from the abstract and description. The concern is therefore confirmatory rather than corrective.","tokens_in":1726,"tokens_out":382,"duration_ms":38356,"concrete_test":"From the paper's expressions for the correlation functions, recompute the model-scale <x_Q> and <x_q> for one heavy meson (e.g., D); compare the ratio <x_Q> / (<x_Q> + <x_q>) against the naive constituent-mass estimate m_Q / (m_Q + m_q). If the model's value shifts by >15% when the wave-function width parameter is varied within its quoted uncertainty range, the dominance result is sensitive to untested model details.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of heavy-constituent dominance is shown via average longitudinal momentum fractions <x> computed at the model scale (and after NLO DGLAP evolution). These <x> values are obtained directly by evaluating the quark-quark correlation functions that define the initial-scale valence PDFs in the light-cone quark model. For heavy-light pseudoscalars the model wave function must encode the large mass asymmetry; if the standard light-cone ansatz (typically tuned for light mesons) under- or over-estimates the momentum carried by the heavy quark, the reported dominance is an artifact of that choice rather than a robust result. Evolution preserves the ordering only if the initial asymmetry is sufficiently large, so the model-scale input remains the decisive step.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates the parton distribution functions of the kaon and heavy pseudoscalar mesons in the light-cone quark model. Initial-scale valence PDFs are obtained by evaluating quark-quark correlation functions, followed by NLO DGLAP evolution to higher scales. Average longitudinal momentum fractions <x> are computed at both the model scale and after evolution; NLO structure functions for the kaon are predicted at EIC-relevant scales, and NLO Drell-Yan cross sections are given for kaon isospin states on Carbon, Tungsten, and Aluminum targets. The central claim is that heavy constituents dominate the momentum fractions in heavy mesons.","tokens_in":1865,"tokens_out":541,"duration_ms":48623,"significance":"If the light-cone model inputs are reliable, the work supplies concrete predictions for upcoming EIC structure-function measurements and COMPASS++/AMBER Drell-Yan data, together with a quantitative statement of heavy-quark momentum dominance that could be tested. The approach of fixing model-scale PDFs and evolving them perturbatively is standard, but the absence of any reported validation, error propagation, or comparison to existing calculations or data limits the immediate utility of the results.","major_comments":[{"comment":"The central claim of heavy-constituent dominance rests on the average momentum fractions <x> evaluated directly from the quark-quark correlation functions that define the initial-scale PDFs (Abstract and workflow description). No validation against experimental constraints, lattice results, or alternative heavy-meson models is presented, so it is impossible to determine whether the reported dominance reflects the meson structure or the specific light-cone ansatz chosen for the heavy-light mass asymmetry.","section":"Abstract / initial-scale PDF construction"},{"comment":"The manuscript supplies no error estimates, scale-variation bands, or sensitivity tests on the model-scale input. Because evolution preserves the ordering only when the initial asymmetry is sufficiently large, the lack of uncertainty quantification on the initial <x> values makes the post-evolution dominance statement difficult to assess quantitatively.","section":"Momentum-fraction and evolution sections"}],"minor_comments":[{"comment":"Notation for the initial scale and the precise definition of the model wave function should be stated explicitly in the main text rather than left implicit in the abstract description.","section":null},{"comment":"Figure captions and table headings should include the numerical values of the model scale and the evolution scale used for each result.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below and indicate the revisions we will make to strengthen the presentation and quantitative support for our results.","responses":[{"response":"We acknowledge that the manuscript does not contain explicit side-by-side comparisons with lattice QCD or other non-perturbative calculations for heavy-meson PDFs. The light-cone quark model parameters are fixed by reproducing the known decay constants and masses of the mesons, which constitute indirect experimental constraints. In the revised version we will add a dedicated paragraph in Section II that recalls prior validations of the same light-cone ansatz for the kaon against available data and that briefly contrasts our <x> values with expectations from heavy-quark effective theory and selected Dyson-Schwinger studies. This addition clarifies that the reported dominance follows from the large mass asymmetry built into the model wave function rather than from an arbitrary choice of functional form.","revision_made":"partial","referee_comment":"[Abstract / initial-scale PDF construction] The central claim of heavy-constituent dominance rests on the average momentum fractions <x> evaluated directly from the quark-quark correlation functions that define the initial-scale PDFs (Abstract and workflow description). No validation against experimental constraints, lattice results, or alternative heavy-meson models is presented, so it is impossible to determine whether the reported dominance reflects the meson structure or the specific light-cone ansatz chosen for the heavy-light mass asymmetry."},{"response":"We agree that the absence of uncertainty quantification limits the ability to judge how robust the dominance conclusion remains under reasonable variations of the model input. In the revised manuscript we will include a new sensitivity study: the constituent quark masses and the transverse-momentum scale parameter of the light-cone wave function are varied within intervals consistent with meson spectroscopy. The resulting spread in the initial-scale <x> values is propagated through the NLO DGLAP evolution and displayed as shaded bands on the relevant figures for both the momentum fractions and the predicted observables. We also add a short paragraph demonstrating that the ordering of <x> is preserved for all variations explored, thereby addressing the referee’s concern about the stability of the post-evolution statement.","revision_made":"yes","referee_comment":"[Momentum-fraction and evolution sections] The manuscript supplies no error estimates, scale-variation bands, or sensitivity tests on the model-scale input. Because evolution preserves the ordering only when the initial asymmetry is sufficiently large, the lack of uncertainty quantification on the initial <x> values makes the post-evolution dominance statement difficult to assess quantitatively."}],"tokens_in":1454,"tokens_out":560,"duration_ms":40686,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper takes the standard light-cone quark model, pulls initial valence PDFs from the quark-quark correlation functions for the kaon plus D and B mesons, runs NLO DGLAP evolution, and then reports average momentum fractions plus concrete predictions for EIC structure functions and COMPASS Drell-Yan on nuclear targets. The central numerical result is that the heavy constituent carries most of the momentum both at the model scale and after evolution. That is the main deliverable: a set of numbers for two near-term experiments rather than a new formalism. The calculations themselves look like a direct, reproducible extension of earlier light-meson work, and the choice to give explicit cross-section predictions for Carbon, Tungsten, and Aluminum targets is useful for people who actually plan those runs. The evolution step is standard and the NLO treatment is appropriate for the scales involved. The soft spot is exactly the one the stress-test flags. The initial PDFs are generated inside the same light-cone ansatz whose outputs are later quoted as evidence. For heavy-light systems the wave function has to encode a large mass asymmetry; if the usual parametrization (tuned on light mesons) already builds in a heavy-quark momentum fraction above 0.5, then the reported dominance is not an independent finding. The abstract gives no sensitivity checks, no comparison to lattice or other model results, and no error bands on the starting scale. Without those, a reader cannot tell whether the ordering survives reasonable variations in the model parameters. The paper is aimed at phenomenologists who need quick estimates for EIC or COMPASS kaon and heavy-meson observables. Someone working on meson structure functions could pull the numbers and test them against data once it arrives. It is not a broad theoretical advance, but the targeted predictions are concrete enough that a serious referee could check the numerics and the heavy-meson modeling assumptions in one pass. I would send it to review rather than desk-reject.","headline":"This extends the light-cone quark model to heavy pseudoscalars with NLO evolution and experiment-specific predictions, but the heavy-quark dominance result tracks directly from the model's own initial-scale inputs.","tokens_in":2354,"tokens_out":479,"would_cite":false,"duration_ms":31264,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"We demonstrate the dominance of the heavy constituents over the lighter constituents within their heavy mesons in terms of their possessed momentum fractions."},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean","rs_theorem":"alpha_pin_under_high_calibration","paper_passage":"The radial wave function of the mesons is expressed as ϕ(x,k²_⊥)=A_h exp[−(k²_⊥+m²_q)/x + (k²_⊥+m²_¯q)/(1−x) / (8β²_h) + …]"}],"headline":"Standard LCQM + NLO DGLAP calculation of heavy-meson PDFs; mass-asymmetric momentum fractions emerge from model wave functions, no RS cost or φ-ladder structure","alignment":"orthogonal","rationale":"The paper's core machinery (BHL radial wave function ϕ(x,k⊥) with parameters m_q, m_¯q, β_h; overlap representation of f_q(x) from quark-quark correlators; NLO DGLAP evolution; <x> moments showing heavy-quark dominance) is a conventional phenomenological QCD model. It contains no J-cost functional, reciprocal symmetry, golden-ratio identities, 8-tick periodicity, or parameter-free derivation of constants. RS theorems (e.g., reality_from_one_distinction, J-uniqueness via Aczél, alpha_pin_under_high_calibration) are therefore neither used nor contradicted; the work lies in the domain of hadronic phenomenology where the RS framework offers no direct prediction.","tokens_in":65290,"confidence":"high","tokens_out":406,"duration_ms":16362,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Heavy constituents carry larger momentum fractions than light ones inside heavy mesons.","keywords":["parton distribution functions","heavy mesons","light-cone quark model","DGLAP evolution","momentum fractions","kaon structure functions","Drell-Yan cross sections"],"falsifier":"An experimental measurement of momentum fractions in a heavy meson at high scales showing the lighter constituent carrying a larger fraction than the heavy one would contradict the dominance result.","tokens_in":2592,"feed_emoji":"","tokens_out":605,"duration_ms":30644,"temperature":0.7,"pith_summary":"The paper calculates the parton distribution functions of the kaon and heavy pseudoscalar mesons in the light-cone quark model. It starts from initial-scale PDFs obtained via quark-quark correlation functions for each meson and evolves them to higher scales using next-to-leading-order DGLAP equations. Average longitudinal momentum fractions for each constituent are computed at both the initial model scale and the evolved scale. The results show that heavy quarks and antiquarks possess greater momentum shares than lighter constituents within heavy mesons. Predictions are also given for kaon structure functions at Electron-Ion Collider energies and for Drell-Yan cross sections in proposed kaon experiments.","feed_headline":"Heavy quarks carry most momentum in heavy mesons","feed_subtitle":"Light-cone model calculations show heavy constituents dominate momentum fractions both at the initial scale and after NLO QCD evolution.","key_machinery":"Light-cone quark model PDFs derived from quark-quark correlation functions, evolved with NLO DGLAP equations to extract constituent momentum fractions.","core_discovery":"Within the light-cone quark model, the initial-scale PDFs of heavy pseudoscalar mesons are constructed from quark-quark correlation functions, then evolved via NLO DGLAP equations; the resulting momentum fractions demonstrate that the heavy quark and antiquark carry larger shares of the total momentum than the lighter constituents both before and after evolution.","pith_inferences":["The same dominance pattern may appear in other heavy-hadron systems once similar model calculations are performed.","Higher-order evolution or lattice comparisons could provide independent checks on the momentum-fraction ordering."],"forward_implications":["Heavy mesons exhibit a partonic structure in which valence heavy quarks dominate the longitudinal momentum.","Kaon structure functions can be predicted at the energy scales of the upcoming Electron-Ion Collider.","Drell-Yan cross sections for both isospin states of the kaon can be computed for nuclear targets such as carbon, tungsten, and aluminum."],"fun_headline_variants":["Heavy quarks dominate meson momentum fractions","Light-cone PDFs show heavy momentum lead","NLO DGLAP confirms heavy constituent lead","Momentum shares favor heavy quarks in mesons"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The initial-scale quark and antiquark PDFs obtained by evaluating the quark-quark correlation functions for individual mesons accurately represent the mesons' partonic structure at the model scale.","fun_headline_variants_meta":{"raw":{"variants":["Heavy quarks dominate meson momentum fractions","Light-cone PDFs show heavy momentum lead","NLO DGLAP confirms heavy constituent lead","Momentum shares favor heavy quarks in mesons"]},"model":"grok-4.3","cost_usd":0.006112,"raw_usage":{"total_tokens":2800,"prompt_tokens":657,"num_sources_used":0,"completion_tokens":52,"cost_in_usd_ticks":61115500,"prompt_tokens_details":{"text_tokens":657,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2091,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":657,"tokens_out":52,"duration_ms":25312,"temperature":1.0,"reasoning_tokens":2091,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-20T13:06:44.560728+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experimental measurement of momentum fractions in a heavy meson at high scales showing the lighter constituent carrying a larger fraction than the heavy one would contradict the dominance result.","supporting_citations":[],"review_version":1}