{"id":"aae9d889-f816-495b-b68d-ad702d466471","arxiv_id":"2505.10663","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"The Lambda and Sigma0 baryon parton distribution functions are predicted from a symmetry-preserving contact-interaction model, showing that the strange quark in Sigma0 needs axialvector diquarks to carry spin.","lead":"A quark-plus-diquark model is used to compute the quark, gluon, and sea distribution functions of the Lambda and Sigma0 baryons. The results show how diquark correlations shape hyperon spin and momentum structure, with predictions that future deep-inelastic experiments could test.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lambda light-quark polarized-DF cancellation is not protected: omitted quark-exchange diagrams could shift helicity into light quarks and alter the central spin decomposition.","rationale":"This is a real but contained model-dependence concern. The paper deserves credit for spelling out the omission and for checking the unpolarised sum rules; the qualitative statements that follow from the SU(3) wave functions, e.g., the Sigma0 s-quark spin requires axialvector diquarks, are much less exposed to this issue. The quantitative Lambda spin decomposition is different: it relies on a cancellation whose scale is comparable to the quoted value. Because the evolution ratio is scale-invariant, this is not a small-zeta detail; it feeds directly into the polarised glue, sea, and the a_0^E numbers that are compared with COMPASS. My recommendation is therefore not to change the reader's CONDITIONAL verdict: the concern does not make the paper rejectable, and the explicit formulas make the missing piece well-defined and computable. The proposed check is exactly the missing calculation the authors themselves defer.","tokens_in":35063,"tokens_out":7224,"duration_ms":76535,"concrete_test":"Compute, in the same SCI framework, the quark-exchange and partner diagrams of Ref. [36, Figs. 4-6] for the Lambda baryon-to-quark DF current and re-evaluate Delta u_Lambda(x; zeta_H), <Delta u/g_A>_Lambda, and the OAM moments in Eq. (75). A decisive threshold is whether <Delta u/g_A>_Lambda moves by more than about 0.05-0.1 from the published -0.018; if it does, the cancellation and the resulting 's carries most of the Lambda spin' decomposition are artifacts of the omitted diagrams, and the quantitative spin predictions should be marked unverified pending that calculation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Read in good faith, the paper is an explicit model calculation whose unpolarised DFs are fixed by number/momentum sum rules. The load-bearing weak point is the Lambda polarized light-quark DF. Eq. (59) reports <Delta l/g_A>_Lambda = -0.018 versus <Delta s/g_A>_Lambda = 0.593, and Section 5.2 explains that this near-cancellation results from four terms, with the [ls] <-> {ls} transition negative and large. The very next paragraph states that the omitted quark-exchange and partner diagrams would have as their principal impact a shift of 'some helicity into light quarks within the Lambda.' No sum rule or symmetry protects the cancellation; the unpolarised number/momentum checks in Eqs. (24),(32) do not constrain helicity. Moreover, Eq. (57) makes the ratio Delta q/q scale-invariant, so a hadron-scale shift propagates unchanged into the evolved polarised glue and sea DFs and into the spin decompositions in Eqs. (75)-(82). Thus the quantitative Lambda spin structure is contingent on an uncalculated current contribution. The authors flag this honestly, but the central quantitative claim about where Lambda spin resides is not yet robust.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends a symmetry-preserving vector×vector contact-interaction (SCI) quark + interacting-diquark treatment to compute helicity-independent and helicity-dependent valence distribution functions of the Λ and Σ0 baryons at the hadron scale, evolves them to 2 GeV using the all-orders scheme, and derives glue and four-flavour separated sea DFs, Mellin moments, and baryon spin decompositions. The core structural input is the different spin-flavour Faddeev wave functions of Λ(I=0) and Σ0(I=1), and the analysis emphasizes observable signatures of scalar versus axialvector diquark content, e.g., the claim that the s quark in Σ0 can carry spin only because of axialvector diquarks. All results follow from meson-sector-tuned SCI parameters and satisfy valence number and momentum sum rules.","tokens_in":35377,"tokens_out":3269,"duration_ms":37746,"significance":"If the results are robust, the paper provides the first extensive, internally consistent set of Λ and Σ0 unpolarised and polarised DFs from a symmetry-preserving quark+diquark framework, including evolved glue and sea distributions and spin decompositions. The strengths are the explicit algebraic formulae, the parameter-free character of the predictions once the SCI parameters are fixed by meson properties, the verification of sum rules, and the provision of interpolation coefficients that make the results reproducible. The paper also makes falsifiable predictions, such as scale-invariant polarised/unpolarised ratios and large-x relations. However, the central quantitative claim about where Λ spin resides rests on a delicate cancellation in the polarised light-quark channel that is not protected by any symmetry and depends on an omitted class of diagrams and on a phenomenological transition DF; this limits the strength of the conclusions that can be drawn from the spin decomposition.","major_comments":[{"comment":"The near-cancellation that produces ⟨Δl/g_A⟩_Λ = −0.018 versus ⟨Δs/g_A⟩_Λ = 0.593 is not protected by any sum rule. The paper itself states in Section 5.2 that the omitted quark-exchange and partner diagrams would shift “some helicity into light quarks within the Λ.” Since Eq. (57) makes Δq(x;ζ)/q(x;ζ) scale invariant, a hadron-scale shift in Δl propagates unchanged into the evolved polarised glue and sea DFs and into the spin decompositions in Eqs. (75)–(82). The unpolarised sum rules in Eqs. (24) and (32) do not constrain this helicity channel. The authors are honest about the omission, but as written the quantitative claim that the Λ spin is predominantly carried by the strange quark, and the related OAM fractions, are contingent on an uncalculated current contribution. I ask the authors either to estimate the size of these diagrams within the SCI, or to reframe the Λ spin conclusions as conditional on this omission.","section":"Section 5.2, Eq. (59)"},{"comment":"The scalar-to-axialvector diquark transition DF, which contributes a large negative term to the Λ polarised light-quark DF through Eqs. (39) and (45), is not computed from the model. Instead, l^01_V(x) is set proportional to the square of a phenomenological “middle” kaon DA of Ref. [53]. The sensitivity of the central Λ cancellation to this ad hoc choice is not tested. The proton analogue in Ref. [18] showed little sensitivity to the [ud]↔{ud} transition DF, but that does not establish the same for the [ls]↔{ls} transition in the Λ, where the cancellation is much more delicate. I request a sensitivity study using alternative transition shapes, or a computed transition DF, before the Λ polarised light-quark result and its spin consequences are presented as definitive.","section":"Appendix A, Eqs. (A.9)–(A.10)"}],"minor_comments":[{"comment":"The column headers for the Σ0 rows repeat the Λ labels “Su_Λ, Sd_Λ, Ss_Λ, Sc_Λ”; these should be Σ0 labels to avoid confusion.","section":"Table 4"},{"comment":"The projector Λ_+ is defined with m_Σ, but the symbol Λ_+ is the same as that used for the Λ baryon in Section 3.1. Using Σ_+ or a different notation would remove needless ambiguity.","section":"Section 3.2, Eq. (26)"},{"comment":"The entry “d/u 0.71/2 = 0.36” is confusing: the convention for comparing single-flavour ratios in Λ/Σ0 with the nucleon’s d/u should be stated clearly in the text or table caption.","section":"Section 5.3, Eq. (61)"},{"comment":"The amplitude normalisation factor n_c^Λ = n_c^Σ = 0.217 is stated, but the unit-normalised coefficients in the table are used directly in later formulae; it would help to make explicit where the canonical normalisation factor enters the DF expressions in Appendices B.","section":"Section 2, Table 3"},{"comment":"The Pauli-blocking modification is applied only to the proton; the text explains why for Λ/Σ0, but the statement could be made earlier in the section to prevent readers from asking whether the same factor should appear in all baryon evolutions.","section":"Section 6, Eq. (63)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically careful and the authors are explicit about the model's limitations, which I regard as a strength. My main concern is that the headline Λ spin result — the near-zero polarised light-quark contribution and the consequent spin decomposition — is not robust to the omitted quark-exchange diagrams and is sensitive to an external input in the transition DF. This is fixable within the scope of the paper by adding sensitivity estimates or by softening the central claims, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the headline: this is the first symmetry-preserving contact-interaction calculation of the full set of Lambda and Sigma0 DFs, and it is a genuinely useful model result. The derivations are explicit, the sum rules are checked, the interpolation tables mean anyone can reconstruct the curves, and the authors are candid about what is missing. Credit where due: the far-valence ratios in Eq. (61) are scale-invariant and give sharp, testable differences between Lambda and Sigma0 that any future calculation can check. The comparison with nucleon DFs is instructive, and the message that axialvector diquarks are needed for the s quark to be visible at large x and to carry Sigma0 spin is a clear structural prediction.\n\nThe soft spot is exactly where the stress-test note points. The Lambda polarised light-quark DF is a near-cancellation of four terms, and the result <Delta l/g_A>_Lambda = -0.018 is not protected by any sum rule. The authors themselves say that the omitted quark-exchange diagrams would shift some helicity into light quarks. Because Delta q/q is scale-invariant, a hadron-scale shift propagates straight into the polarised glue, the sea, and the spin decomposition. So the quantitative Lambda spin fractions — and the statement that the s quark carries most of the spin — are contingent on an uncalculated current contribution. That is not a fatal flaw if the claims are framed as model predictions, and the authors do flag it. But it does mean the central quantitative spin result is not yet robust.\n\nThe other approximations are minor by comparison. The [ls] to {ls} transition DF is borrowed from a kaon DA rather than computed; the authors point to the proton analogue where sensitivity was small, which is plausible but not a substitute. The static axial approximation underestimates gA; they correct for it when reporting absolute spin fractions. The citation pattern looks honest: the inputs come from meson-sector fits and prior baryon analyses, and nothing is fitted to the target observables.\n\nFor a reader who wants a coherent model prediction for hyperon DFs, this paper delivers. For a reader who wants a robust statement about Lambda spin, it is not there yet — but the paper says so. I would take it seriously as a peer-reviewed model calculation: send to a referee who can push on the quark-exchange estimate, and ask the authors to either compute or bound the omitted diagrams or to soften the Lambda spin claims accordingly.","headline":"First SCI prediction of Lambda/Sigma0 DFs, with a load-bearing caveat on the Lambda polarised light-quark cancellation.","tokens_in":35891,"tokens_out":2775,"would_cite":true,"duration_ms":27494,"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 predicts the $\\Lambda$ and $\\Sigma^0$ baryons' valence, glue, and sea distribution functions from a quark+diquark contact interaction, showing that diquark correlations imprint spin-flavour signatures—notably, the $\\Sigma^0$'s…","keywords":["Lambda baryon","Sigma0 baryon","parton distribution functions","polarised distributions","diquark correlations","contact interaction","spin decomposition","all-orders evolution"],"falsifier":"Recompute the $\\Lambda$ and $\\Sigma^0$ DFs with the quark-exchange diagram and its partner diagrams included in the interaction current (the diagrams omitted here); the central claim fails if the $\\Lambda$ polarised light-quark DF's first moment is no longer near zero or the $\\Sigma^0$ strange-quark spin fraction changes sign. A less direct check is unquenched lattice QCD for $\\langle x\\rangle_s^\\Lambda$ and $a_0^{\\Lambda,\\Sigma^0}$ disagreeing with the paper's Table 4 beyond uncertainties.","tokens_in":34849,"feed_emoji":"⚛️","tokens_out":7175,"duration_ms":64806,"temperature":0.7,"pith_summary":"This paper claims that the internal parton structure of the $\\Lambda$ and $\\Sigma^0$ baryons is set, to a large degree, by their spin-flavour wave functions, in which the same three valence quarks $(u,d,s)$ are arranged differently: the $\\Lambda$ is dominated by an $s$ quark plus a scalar $[ud]$ diquark, while the $\\Sigma^0$ has more axialvector-diquark strength. Using a symmetry-preserving contact interaction with quark-plus-interacting-diquark bound states, the authors compute unpolarised and polarised valence, glue, and four-flavour separated sea distribution functions at the hadron scale and evolve them to 2 GeV. The results expose clear diquark signatures: for instance, the $\\Sigma^0$'s strange quark would carry none of the baryon's spin if axialvector diquarks were absent, and the $\\Lambda$'s polarised light-quark distribution nearly cancels. The authors argue that these predictions, if confirmed, tie baryon spin decompositions and hard-scattering observables to emergent hadron mass and diquark correlations.","feed_headline":"Sigma0's strange quark gets its spin from axialvector diquarks","feed_subtitle":"A quark-diquark contact calculation maps Lambda and Sigma0 quark, glue, and sea distributions and spin fractions at 2 GeV.","key_machinery":"The load-bearing object is the Poincar\\'e-covariant quark-plus-interacting-diquark Faddeev amplitude for octet baryons, built from scalar $[ud]$, $[ls]$ and axialvector $\\{ud\\}$, $\\{ls\\}$ diquark correlations with masses and amplitudes fixed by meson-tuned SCI parameters. Distribution functions are computed at the hadron scale $\\zeta_H$, defined as the scale where all baryon momentum and spin reside in valence quasiparticles, so glue and sea DFs vanish there; all-orders evolution then undresses the valence quarks and generates glue and sea. The algebraic SCI formulae make the mechanism transparent: baryon-number and momentum sum rules follow from identities relating struck-quark terms to diquark momentum distributions, and helicity dependence enters through dressed-quark axial charges and axialvector-diquark transition form factors. This machinery converts the spin-flavour wave functions of Eqs. (1a) and (1b), rather than fitted parton parameters, into the shapes and moments of the DFs.","core_discovery":"Within a symmetry-preserving treatment of a vector$\\times$vector contact interaction, the paper derives hadron-scale valence-quark DFs for $\\Lambda$ and $\\Sigma^0$ from their Faddeev amplitudes, then uses all-orders evolution to predict glue and sea DFs at $\\zeta_2=2$ GeV. The central discovery is that the different diquark content of the two isospin partners leaves measurable signatures: the $\\Sigma^0$ $s$-quark DF resembles half the neutron's $d$-quark DF, the $\\Lambda$ light-quark DF resembles the neutron's $u$ DF, and the polarised $\\Lambda$ light-quark DF is nearly zero because large positive and negative contributions cancel. The most qualitative claim is that only the presence of axialvector diquarks allows the $\\Sigma^0$'s strange quark to be struck by a hard probe or to carry spin; without them it would be sequestered inside an unpolarisable scalar diquark. Evolved spin decompositions put quark helicity at about 51% of the $\\Lambda$ spin, 44% of the $\\Sigma^0$ spin, and 45% of the proton spin at 2 GeV, with glue contributing about 41% in each case.","pith_inferences":["If the wave-function signatures survive a calculation that includes the omitted quark-exchange diagrams, then polarised $\\Lambda$ electroproduction spin-transfer measurements, once reliable fragmentation functions exist, would provide a direct experimental test of diquark content.","The near-cancellation of the $\\Lambda$'s polarised light-quark DF is the most fragile prediction; including the omitted diagrams could flip its sign, changing $\\ell^q_\\Lambda$ and the inferred quark-orbital-angular-momentum fraction without necessarily disturbing the unpolarised DFs.","Because the SCI produces explicit interpolation coefficients and Mellin moments, unquenched lattice QCD calculations of $\\langle x\\rangle_s^\\Lambda$ and $a_0^{\\Lambda,\\Sigma^0}$ could settle the comparison suggested in the paper; the authors already note that the quenched lattice moments should be revisited.","The same machinery, applied to decuplet baryons or singly-heavy baryons, would sharpen the diquark signatures because those wave functions are simpler and the scalar-versus-axialvector competition is more extreme."],"forward_implications":["The $\\Sigma^0$'s strange quark can be a valence degree of freedom seen by hard probes only because axialvector diquarks exist; on $x\\simeq1$, ratios like $l/s$ and $\\Delta l/\\Delta s$ would otherwise diverge.","The $\\Lambda$ polarised light-quark DF is predicted to be almost zero at the hadron scale, so almost all of the $\\Lambda$'s helicity is carried by the strange quark, with light-quark orbital angular momentum accommodating the remainder.","After evolution, glue and sea DFs in $\\Lambda$, $\\Sigma^0$, and proton are very similar in shape, with the same net gluon contribution to spin ($\\approx 41\\%$); the $\\Lambda$ has about 13% more polarised glue than the proton and the $\\Sigma^0$ about 3% less.","Higgs-generated mass differences between $s$ and light quarks are largely masked by emergent mass, so the $s$ quark carries only about 30% more momentum than each light quark in the $\\Lambda$ and about 5% more in the $\\Sigma^0$.","The predicted spin fractions at 2 GeV place contemporary proton spin data inside the model's band, offering a resolution of the proton spin crisis in which quark helicity, quark orbital angular momentum, and gluon angular momentum all contribute."],"supporting_citations":[{"why":"provides the SCI nucleon DF analysis whose methods, sum rules, and nucleon curves the present calculation adapts and compares against.","marker":"[18]"},{"why":"supplies the SCI diquark masses, amplitudes, Faddeev solutions, and axial form factors used in the DF formulae.","marker":"[36]"},{"why":"defines the all-orders evolution scheme and the hadron-scale concept that convert hadron-scale valence DFs into glue and sea.","marker":"[37]"},{"why":"establishes the hadron-scale notion for mesons and supplies the kaon distribution-amplitude form used for the scalar-axialvector transition DF.","marker":"[53]"},{"why":"provides the counterpoint proton and pion DF analysis and the large-x power behaviour used as a consistency check.","marker":"[16]"},{"why":"gives the light-diquark distribution amplitudes used in Appendix A for the diquark valence-quark DFs.","marker":"[104]"},{"why":"supplies lattice estimates of octet-baryon axial charges that the SCI $a_0$ ratios are compared with.","marker":"[30]"},{"why":"provides the quenched lattice $\\Lambda$ momentum fractions that the paper suggests should be revisited in light of its predictions.","marker":"[28]"}],"fun_headline_variants":["Axialvector diquarks give Sigma0's strange quark its spin","Lambda and Sigma0 structure reveals diquark fingerprints","Without axialvector diquarks, Sigma0's strange quark stays hidden","Diquark composition shapes baryon spin and parton distributions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predicted $\\Lambda$ polarised light-quark cancellation and the resulting spin decomposition rest on omitting quark-exchange (and partner) diagrams from the baryon-to-quark interaction current; if those diagrams shift helicity into light quarks, that prediction changes.","fun_headline_variants_meta":{"raw":{"variants":["Axialvector diquarks give Sigma0's strange quark its spin","Lambda and Sigma0 structure reveals diquark fingerprints","Without axialvector diquarks, Sigma0's strange quark stays hidden","Diquark composition shapes baryon spin and parton distributions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001135,"raw_usage":{"total_tokens":4772,"prompt_tokens":1059,"completion_tokens":3713,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":675,"completion_tokens_details":{"reasoning_tokens":3640}},"tokens_in":675,"tokens_out":3713,"duration_ms":24404,"temperature":1.0,"reasoning_tokens":3640,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:06:33.483899+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the $\\Lambda$ and $\\Sigma^0$ DFs with the quark-exchange diagram and its partner diagrams included in the interaction current (the diagrams omitted here); the central claim fails if the $\\Lambda$ polarised light-quark DF's first moment is no longer near zero or the $\\Sigma^0$ strange-quark spin fraction changes sign. A less direct check is unquenched lattice QCD for $\\langle x\\rangle_s^\\Lambda$ and $a_0^{\\Lambda,\\Sigma^0}$ disagreeing with the paper's Table 4 beyond uncertainties.","supporting_citations":[{"cited_title":"Cheng, F","cited_arxiv_id":null,"evidence_quote":"supplies the SCI diquark masses, amplitudes, Faddeev solutions, and axial form factors used in the DF formulae."},{"cited_title":"Yin, Y.-Z","cited_arxiv_id":null,"evidence_quote":"defines the all-orders evolution scheme and the hadron-scale concept that convert hadron-scale valence DFs into glue and sea."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"gives the light-diquark distribution amplitudes used in Appendix A for the diquark valence-quark DFs."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies lattice estimates of octet-baryon axial charges that the SCI $a_0$ ratios are compared with."},{"cited_title":"Gockeler, R","cited_arxiv_id":null,"evidence_quote":"provides the quenched lattice $\\Lambda$ momentum fractions that the paper suggests should be revisited in light of its predictions."}],"review_version":1}