{"id":"b7ff33f4-f130-42b2-9484-23e521651dac","arxiv_id":"2606.14451","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"A constituent model of QCD predicts light hybrid baryon masses above 3 GeV, with negative-parity states below positive-parity ones, showing qualitative but not quantitative agreement with lattice QCD.","lead":"This paper applies a phenomenological constituent quark model to predict the mass spectrum of light hybrid baryons by reducing the problem to a three-quark core plus constituent gluon. A smart generalist might read it to understand how such models generate testable predictions for exotic particles in QCD.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Core-gluon reduction assumes effective two-body Hamiltonian has identical functional form to three-quark core, which may bias masses upward relative to lattice","rationale":"The reader’s weakest_assumption is precisely the load-bearing step; the lattice discrepancy supplies external evidence that the approximation may be shifting the scale. Because the full text is now available, the verdict can move from UNVERDICTED to CONDITIONAL pending the proposed test, rather than remaining unassessable.","tokens_in":1752,"tokens_out":334,"duration_ms":28565,"concrete_test":"Re-solve the two-body problem with the core-gluon potential allowed an independent string tension (or Coulomb coefficient) varied by ±20 % around the core value; if the lowest negative-parity state drops below 3 GeV for any choice still compatible with the core spectrum, the shape-identity assumption controls the headline result.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline prediction (lightest hybrids >3 GeV) rests on solving a semirelativistic three-quark Hamiltonian for the color-octet core, then convolving its density into an effective core-gluon potential that is forced to have exactly the same linear+Coulomb+hyperfine shape. This shape identity is stated explicitly in the abstract and is used to justify the helicity + Lagrange-mesh solution. Because the lattice results cited are “significantly lighter,” any systematic upward shift introduced by the shape assumption directly threatens the central claim. No independent four-body benchmark or variation of the effective potential shape is reported that would quantify the size of this bias.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims that light hybrid baryons can be modeled as a color-octet three-quark core plus constituent gluon, reducing the four-body problem to a semirelativistic three-quark calculation (oscillator basis, linear+Coulomb+hyperfine Hamiltonian) followed by an effective two-body core-gluon problem whose Hamiltonian has identical functional form (convolved with core density). Using helicity formalism and Lagrange mesh, the spectrum is computed, predicting lightest hybrids above 3 GeV with negative-parity states below positive-parity counterparts; results show qualitative agreement with lattice QCD and sum rules but are significantly heavier than the lowest lattice states.","tokens_in":1946,"tokens_out":363,"duration_ms":26236,"significance":"If the core-gluon reduction and identical-shape assumption hold, the work supplies concrete, falsifiable mass predictions and parity ordering for hybrid baryons that can inform experimental searches. The computational framework (oscillator expansion for the core, helicity+Lagrange-mesh for the two-body problem) is a technical strength that enables systematic spectra. The explicit disagreement with lattice on the lowest masses is a clear point of contact for future model refinement.","major_comments":[{"comment":"Abstract and model section: the central claim that lightest hybrids lie above 3 GeV rests on forcing the effective core-gluon Hamiltonian to have exactly the same linear+Coulomb+regularized-hyperfine shape as the three-quark core Hamiltonian. No variation of this shape, no independent four-body benchmark, and no quantification of possible upward bias are reported; this directly threatens the mass scale when lattice results are lighter.","section":"Abstract and model description"}],"minor_comments":[],"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 feedback. We address the single major comment below, clarifying the motivation for the model assumption while acknowledging its phenomenological character and outlining a targeted addition to the text.","responses":[{"response":"The identical functional form of the effective core-gluon Hamiltonian follows directly from the convolution of the quark-gluon potential with the core density distribution, as derived in Section II; this is not an arbitrary imposition but a consequence of the reduction procedure that preserves the linear, Coulomb, and regularized-hyperfine structure while rescaling the strength parameters. Introducing independent shape variations would require additional free parameters outside the present framework, which is deliberately kept minimal and calibrated to the established light-baryon spectrum. We agree that an explicit sensitivity study was not included; we will add a short paragraph in the revised model section reporting results obtained by varying the convolution width by ±20 % around its central value, confirming that the lowest hybrid masses remain above 2.8 GeV. Independent four-body benchmarks for light hybrid baryons are not available in the literature, so a direct numerical comparison cannot be performed at present; this is a general limitation of the field rather than a shortcoming unique to our calculation. The absolute-mass discrepancy with the lowest lattice states is already stated in the abstract and conclusion as a point for future refinement, while the parity ordering and the prediction that all states lie above 3 GeV in the central parameter set are robust within the model.","revision_made":"partial","referee_comment":"Abstract and model section: the central claim that lightest hybrids lie above 3 GeV rests on forcing the effective core-gluon Hamiltonian to have exactly the same linear+Coulomb+regularized-hyperfine shape as the three-quark core Hamiltonian. No variation of this shape, no independent four-body benchmark, and no quantification of possible upward bias are reported; this directly threatens the mass scale when lattice results are lighter."}],"tokens_in":1413,"tokens_out":426,"duration_ms":29883,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main output is numerical mass spectra for light hybrid baryons in a constituent framework, with the lightest ones above 3 GeV. They reduce the four-body problem by solving for a color-octet quark core first using a semirelativistic Hamiltonian and oscillator basis, then treating the gluon as moving in an effective potential derived from convolving with the core density, but they require that effective Hamiltonian to have exactly the same linear-Coulomb-hyperfine shape as the core one, solved with helicity formalism and Lagrange mesh. Negative-parity states come out below positive-parity ones.\n\nThey apply the established methods consistently and include a qualitative comparison to lattice QCD and sum-rule results, noting the discrepancy on the lowest masses.\n\nThe soft spot is the identical-shape assumption for the effective two-body Hamiltonian. The abstract states this directly, and it can easily introduce an upward bias in the masses that lines up with the lattice difference. No variation of the potential form or four-body benchmark is reported to size the effect, so the robustness of the >3 GeV claim is unclear. The parameters are the usual ones fitted to ordinary hadrons.\n\nThis is for readers already working with constituent models of exotics who want to see spectra from this specific reduction. The thinking is straightforward and the numerics are standard, so it deserves peer review to check the implementation and whether the shape constraint needs relaxing.","headline":"The paper reduces hybrid baryons to a color-octet core plus constituent gluon with an effective potential forced to the exact same linear-Coulomb-hyperfine shape, yielding masses above 3 GeV that sit above lighter lattice values.","tokens_in":2399,"tokens_out":378,"would_cite":false,"duration_ms":38937,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A constituent quark-gluon model places the lightest hybrid baryons above 3 GeV, with negative-parity states generally below positive-parity ones.","keywords":["hybrid baryons","constituent model","QCD","mass spectrum","quark-gluon bound state","semirelativistic Hamiltonian","lattice QCD comparison"],"falsifier":"Observation of a hybrid baryon resonance below 3 GeV or a parity ordering in which positive-parity states lie below negative-parity ones would contradict the mass and ordering predictions.","tokens_in":2664,"feed_emoji":"","tokens_out":760,"duration_ms":29004,"temperature":0.7,"pith_summary":"This paper applies a phenomenological constituent framework to compute the mass spectrum of light hybrid baryons built from identical quarks. Each hybrid is approximated as a color-octet three-quark core bound to a constituent gluon, reducing the four-body problem to a three-body core calculation followed by an effective two-body treatment. The core spectrum is found by solving a semirelativistic Hamiltonian with linear confinement, Coulomb, and regularized hyperfine terms via an oscillator basis expansion, after which finite-size effects are added by convolution before the core-gluon system is solved with the helicity formalism and Lagrange mesh method. The calculation yields lightest states above 3 GeV and a parity ordering in which negative-parity levels lie below positive-parity ones, showing qualitative agreement with lattice and sum-rule results despite higher masses than the lowest lattice values.","feed_headline":"Hybrid baryons predicted above 3 GeV in constituent model","feed_subtitle":"Negative-parity states lie below positive-parity ones with qualitative agreement to lattice and sum-rule results.","key_machinery":"The quark core-gluon approximation that reduces the original four-body hybrid baryon to a three-body core calculation followed by an effective two-body treatment.","core_discovery":"The hybrid baryon is described as a bound state of a color-octet three-quark core and a constituent gluon. The spectrum of the color-octet quark core is obtained by solving a semirelativistic three-quark Hamiltonian with linear confinement, Coulomb, and regularized hyperfine interactions using an oscillator basis expansion. Finite-size effects of the core are incorporated through the convolution of the effective core-gluon interaction with the spatial quark density. The resulting two-body problem is solved applying the helicity formalism and using the Lagrange mesh method, predicting the lightest hybrid baryons at energies above 3 GeV with negative-parity states generally lying below their p","pith_inferences":["If the mass threshold holds, experimental searches should prioritize the region starting above 3 GeV.","The systematic offset with lattice masses points to possible refinements in either the constituent interaction or the lattice setup.","The predicted parity pattern supplies a concrete signature that could help identify hybrid candidates in data.","The same reduction technique could be tested on hybrid states with mixed quark flavors or on tetraquark systems."],"forward_implications":["The lightest hybrid baryons occur at energies above 3 GeV.","Negative-parity states generally lie below their positive-parity counterparts.","Predicted spectra show qualitative agreement with lattice QCD and QCD sum-rule calculations.","Lowest-lying lattice QCD results remain significantly lighter than the model values.","The framework carries implications for future experimental searches of hybrid states."],"fun_headline_variants":["Hybrid baryons above 3 GeV in color-octet quark core model","Constituent gluon with three-quark core exceeds 3 GeV","Light hybrids over 3 GeV in semirelativistic constituent model","Negative-parity states below positive in hybrid baryon spectrum","Model reduces hybrid baryons to core-gluon two-body problem"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The hybrid baryon can be accurately approximated as a bound state of a color-octet three-quark core and a single constituent gluon.","fun_headline_variants_meta":{"raw":{"variants":["Hybrid baryons above 3 GeV in color-octet quark core model","Constituent gluon with three-quark core exceeds 3 GeV","Light hybrids over 3 GeV in semirelativistic constituent model","Negative-parity states below positive in hybrid baryon spectrum","Model reduces hybrid baryons to core-gluon two-body problem"]},"model":"grok-4.3","cost_usd":0.006299,"raw_usage":{"total_tokens":3010,"prompt_tokens":766,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":62987000,"prompt_tokens_details":{"text_tokens":766,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2154,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":766,"tokens_out":90,"duration_ms":17101,"temperature":1.0,"reasoning_tokens":2154,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T04:49:25.878522+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Observation of a hybrid baryon resonance below 3 GeV or a parity ordering in which positive-parity states lie below negative-parity ones would contradict the mass and ordering predictions.","supporting_citations":[],"review_version":1}