{"id":"545e9b29-3c72-4ffd-97b2-5a44a74b3b96","arxiv_id":"2508.08776","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Embedding diquarks in static-light-light baryons on the lattice gives gauge-invariant evidence that the good diquark is lightest and spherical, with a preliminary trend supporting heavy-quark spin symmetry.","lead":"Lattice QCD calculations of baryons containing a very heavy spectator quark show that the 'good' diquark configuration is the lightest and appears spherical. The approach offers a gauge-invariant way to measure diquark properties that are otherwise invisible in experiment.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified.","rationale":"The reader's weakest_assumption centers on the O(1/m_Q) cancellation in Eq. (4). In the static limit used throughout the paper, m_Q is set to infinity by the static propagator, so the O(1/m_Q) correction is exactly zero; the mass differences are physical splittings of static-light-light baryons, not quantities that depend on a finite heavy-mass expansion. The author explicitly restricts the diquark-probe interpretation to the q q' Q case, and the density-density correlations provide an independent, more direct handle on the two-quark attraction. The main remaining limitations are lattice-systematic in nature: a single lattice spacing, no continuum limit, and a chiral extrapolation ansatz. These are acknowledged in the text and could shift the quantitative values of the splittings, but they are very unlikely to change the qualitative ordering or the observed growth trend, which are the core of the central claim. The paper is a proceedings contribution that transparently defers numerical details to [5], and its claims are appropriately scoped. I therefore see no load-bearing concern that would warrant changing the reader's ACCEPT verdict.","tokens_in":7110,"tokens_out":9011,"duration_ms":100187,"concrete_test":"Perform the same bad/good splitting analysis on a second lattice spacing ensemble (e.g., PACS-CS a ≈ 0.12 fm) and verify that the sign of all splittings and the growth trend toward the physical pion mass survive a naive continuum extrapolation; additionally, where possible, compare with a finite but very heavy spectator such as the b quark to test the static-limit interpretation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the good diquark is the lightest of the studied channels and that the bad/good splitting grows toward the physical quark mass is supported by gauge-invariant lattice data on static-light-light baryons. The reader's concern about Eq. (4) is not load-bearing: the static propagator sets m_Q = infinity by construction, so the O(m_Q^{-1}) term vanishes exactly, and the mass differences are well-defined static-light-light baryon mass splittings. The interpretation as a diquark property is further corroborated by density-density correlations that show spatial attraction in the good-diquark channel and a spherical shape with a static spectator, as presented in the paper and in the earlier reference [5]. The paper openly acknowledges its limitations, including the absence of a continuum extrapolation and the preliminary nature of the HQSS ratio and shape-correlation results, and none of these threaten the qualitative conclusion. No critical assumption appears unsecured.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings paper reports a lattice QCD study of diquark properties using a gauge-invariant embedding of a diquark in a static-light-light baryon. Calculations are performed on n_f=2+1 PACS-CS ensembles at a single lattice spacing (a=0.090 fm) with pion masses from 707 MeV down to 164 MeV. The author extracts mass splittings between the good, bad, and not-even-bad diquark channels, finding that the good diquark is the lightest and that the bad/good splitting increases toward the physical quark mass. The paper also presents preliminary results on a heavy-quark-spin-symmetry (HQSS) test via the ratio M_Omega/M_delta and on radial versus tangential density-density correlations, which indicate quark-quark attraction in the good-diquark channel with a spherical shape for a static spectator and a distorted shape when the spectator is a strange quark.","tokens_in":7267,"tokens_out":9395,"duration_ms":103049,"significance":"If the results are correct, the paper provides a concrete gauge-invariant lattice methodology for isolating diquark physics and offers quantitative evidence supporting the phenomenological picture of a light good diquark with an attractive interaction. The main strengths are: (i) the static spectator eliminates the O(1/m_Q) uncertainty in the mass decomposition, (ii) the use of publicly available ensembles with light pions close to the physical point, (iii) the complementary density-density correlation probes, and (iv) the explicit acknowledgment of known limitations such as the lack of a continuum extrapolation and the preliminary nature of the HQSS and shape analyses. The central claim is falsifiable and appears to be directly supported by the plotted effective-mass data. The paper's honesty about the preliminary status of several results is commendable and appropriate for a proceedings contribution.","major_comments":[],"minor_comments":[{"comment":"The fit parameters for the bad/good and good/quark splitting Ansatze (A, B, n, C, D, n') are not reported in this paper; since the conclusion that the bad/good splitting grows toward the physical point depends on the fitted trend, please provide at least the central values of the physical-point extrapolations and their uncertainties, or state explicitly that they are available in reference [5].","section":"Section 3, chiral extrapolation"},{"comment":"The axis labels, units, and legend entries of Figure 2 are not described in the text; the reader cannot judge the absolute size of the splittings (e.g., whether they are in MeV) or which curves correspond to which channels. Please make the figure self-explanatory or describe it fully in the caption.","section":"Section 3, Fig. 2"},{"comment":"The derivation of the HQSS expectation M_Omega_q/M_delta_q = 3 is not given; as written, the equality seems to follow from the dressed-quark decomposition M_Omega_q = 3 m_q and M_delta_q = m_q rather than directly from heavy-quark spin symmetry. Please clarify this assumption to avoid overstating the connection to HQSS.","section":"Section 2, Eq. (8)"},{"comment":"The definitions of the radial and tangential correlation lengths r_parallel and r_perpendicular are abbreviated; the text states that r_R = r_S + r_r(phi) but does not explicitly define r_parallel and r_perpendicular. A short explicit formula would improve clarity.","section":"Section 2, density correlations"},{"comment":"The manuscript contains corrupted glyphs (for example, 'fix', 'fi0', and 'D' with missing subscripts) that appear to arise from PDF text extraction; please ensure the submission compiles cleanly. Also, 'nt = 2+1' in Section 3 should be 'n_f = 2+1'.","section":"General formatting"}],"recommendation":"minor_revision","confidential_remarks":"The paper is a well-posed proceedings contribution that relies heavily on the author's earlier paper [5] for technical details, which is acceptable for this format. The central claim is supported by the data shown, and the limitations are openly stated. The only requested changes are presentation-level clarifications, so I would be happy to see the paper accepted after minor revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—\n\nThis is an honest, modest conference proceedings, and the right response is to take it as such. It is not a new research paper: the diquark mass splittings in Fig. 2 (top) restate the same author's JHEP 2022 paper [5], and the paper says so. The genuinely new pieces are two preliminary results: the M_Omega_q/M_delta_q ratio as an HQSS test, and radial-vs-tangential density correlations in the uds system. Both are labeled preliminary, with large uncertainties, and neither supports a quantitative conclusion yet.\n\nCredit where it is due: the central qualitative claim is supported by the plotted lattice data. In a gauge-invariant static-light-light setup, the good diquark is lighter than all other channels; the bad/good splitting grows toward the physical pion mass; and the ud channel splits more than us or ss. The density-density correlations show an exponential decay in the good-diquark channel and, with a static spectator, no obvious radial/tangential asymmetry. The paper is also honest about its limitations: no continuum extrapolation, chiral extrapolation fits and parameters deferred to [5], and the two new results called preliminary. No circular reasoning is hiding in the analysis—the splittings come from correlator fits, not from assuming the conclusion.\n\nSoft spots, in proportion: (1) The paper is not self-contained for the quantitative core; the fit Ansatze are written down but the fit parameters and numerical values are only in [5]. For a proceedings this is acceptable, but it limits what a reader can verify from this text. (2) The uds shape distortion is supported by two slopes that look different by eye on one ensemble; no ratio or uncertainty is given. The text says \"possible distortion,\" which is the right level of claim. (3) The HQSS ratio has one ensemble and errors large enough that the charm point is within 1 sigma of the predicted 3. A \"trend\" is about all one can say. (4) The reader's concern about the O(1/m_Q) term in Eq. (4) is not load-bearing: a static quark sets m_Q=infinity by construction, so that term is exactly zero. The mass differences are well-defined static-light-light baryon splittings. The interpretive step from splitting to \"diquark property\" is the place to be cautious, and the paper is appropriately cautious there.\n\nCitation pattern is fine; [5] is the natural predecessor and the heavy self-reliance is justified. I would bring this to a reading group as a compact, honest example of a preliminary-results proceedings, and I would accept it for peer review at the proceedings level. For a journal article I would want the two new pieces completed with more ensembles and a full error budget.\n\n—","headline":"Honest, modest proceedings that restates earlier diquark splittings and adds two clearly preliminary results; fine for a proceedings, too thin for a journal article.","tokens_in":7801,"tokens_out":4106,"would_cite":false,"duration_ms":44807,"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":"Lattice QCD confirms that the 'good' diquark is the lightest diquark channel, with the bad/good splitting growing toward the physical quark mass.","keywords":["diquarks","lattice QCD","static quark","good diquark","mass splitting","quark-quark correlations","heavy-quark spin symmetry","baryon structure"],"falsifier":"Compute the bad/good diquark mass splitting on the same gauge ensembles using a different discretization of the static quark (for example, a different smearing or action); if the extracted splitting moves by more than the quoted uncertainties, the $O(m_Q^{-1})$ cancellation assumption is violated. Alternatively, higher-statistics data at the physical pion mass showing the splitting decreasing toward zero, or radial and tangential correlation radii differing in the static case, would contradict the claimed attractive, spherical good diquark.","tokens_in":6888,"feed_emoji":"⚛️","tokens_out":9489,"duration_ms":87137,"temperature":0.7,"pith_summary":"Lattice QCD is used to test whether diquarks — correlated pairs of quarks inside hadrons — are real, gauge-invariant degrees of freedom. The author embeds a diquark in a baryon that also contains a static (infinitely heavy) spectator quark, so that mass differences between diquark channels can be read off directly from correlation-function ratios without fixing a gauge. The central result is that the 'good' diquark, a spin-0 color-anti-triplet pair, is lighter than every other diquark configuration, and the mass gap between the good and 'bad' diquarks grows as the light quark mass approaches its physical value. This growing splitting is taken as evidence for a real attractive interaction between the two light quarks in the good diquark. Spatial density correlations support the picture: only the good diquark shows an exponential decay characteristic of attraction, and in the static limit the pair is spherical, with no polarization from the spectator.","feed_headline":"Lattice QCD finds the 'good' diquark is lighter than all rivals","feed_subtitle":"A static-spectator calculation shows the attractive quark pair and a growing bad/good mass split.","key_machinery":"The central object is the static-light-light baryon correlation function $C_\\Gamma(t)=\\langle [D_\\Gamma Q](t)[D_\\Gamma Q]^\\dagger(0)\\rangle$, whose long-time behavior is written as $C_\\Gamma(t)\\sim \\exp[-t(m_{D_\\Gamma}+m_Q+O(m_Q^{-1}))]$. Setting $m_Q=\\infty$ (a static quark) makes $O(m_Q^{-1})=0$, so ratios of correlators yield mass differences between diquark channels directly, e.g. $M_{\\mathrm{bad}}-M_{\\mathrm{good}}$, with no gauge fixing. The companion observable is the density-density correlation $C^d_\\Gamma(\\vec{x}_1,\\vec{x}_2,t)$, which measures the spatial distribution of the two light quarks around the spectator and gives effective correlation radii; equality of radial and tangential radii signals a spherical diquark.","core_discovery":"The paper's central claim is that, in a gauge-invariant lattice setup with a static spectator quark, the 'good' diquark configuration is the lightest of all possible diquark channels, and the splitting between the bad and good diquarks increases as the light quark mass approaches its physical value. The author argues this growing splitting is a physical QCD property indicating real attraction between the two light constituent quarks. The same calculation also shows, through spatial quark-quark density correlations, that only the good diquark channel exhibits the exponential decay expected from an attractive correlation, and that with a static spectator the diquark has no preferred radial or tangential correlation direction, implying a spherical shape. Replacing the static spectator with a strange quark distorts this shape, suggesting spectator–diquark polarization, though the precision is still too low for a firm conclusion.","pith_inferences":["The same static-spectator trick could define gauge-invariant masses for other colored clusters, such as a 'triquark' in a doubly heavy baryon, extending the method beyond diquarks.","If the bad/good splitting continues to grow toward the chiral limit at fixed lattice spacing, the growth could be affected by the pion cloud; computing the splitting on finer lattices would test whether the trend survives the continuum limit.","The spherical shape of the good diquark with a static spectator provides a boundary condition for quark models: any model that treats the diquark as compact and pointlike must reproduce both the lightest mass and the isotropic correlation length, while the strange-spectator distortion quantifies the spectator–diquark interaction strength.","The ratio $M_{\\Omega_q}/M_{\\delta_q}$ could serve as a practical diagnostic in lattice calculations that use heavy-quark expansions: deviations from 3 would signal that the practice of dividing the rest-mass parameter by the number of heavy quarks is unreliable."],"forward_implications":["The growing bad/good splitting toward the physical quark mass is a concrete lattice prediction that can be tested against future, higher-statistics data at the physical point.","The spherical shape of the good diquark in the static limit means that, with an infinitely heavy spectator, the diquark is not polarized by the surrounding hadron, simplifying its use as an effective degree of freedom.","The observed distortion when the static spectator is replaced by a strange quark indicates that in ordinary light baryons the diquark shape is influenced by the spectator, so diquark phenomenology in nucleons must account for that interaction.","The preliminary behavior of the ratio $M_{\\Omega_q}/M_{\\delta_q}$ is consistent with heavy-quark spin symmetry, supporting the dressed-quark decomposition of heavy hadrons used in some lattice QCD calculations."],"supporting_citations":[{"why":"Previous full-QCD diquark study that supplies the method, the chiral extrapolation fits, and the numerical values the present work extends and confirms.","marker":"[5]"},{"why":"Phenomenological review that predicts the good diquark to be special and the mass splittings to be physical QCD properties, providing the expectation the lattice result is compared with.","marker":"[2]"},{"why":"Introduces the density-density correlation observable used to search for diquark attraction in hadrons.","marker":"[11]"},{"why":"Provides earlier lattice evidence for diquarks in hadrons, the basis for the correlation approach.","marker":"[12]"},{"why":"Studies spatial diquark correlations in a hadron, informing the radial and tangential geometry of the density correlations.","marker":"[14]"},{"why":"Supplies the $n_f=2+1$ full QCD gauge ensembles on which all calculations are performed.","marker":"[15]"},{"why":"Redetermines the lattice spacing on those ensembles, fixing the physical scale for the mass splittings.","marker":"[16]"}],"fun_headline_variants":["Good diquark stays lightest in lattice QCD with heavy spectator","Lattice QCD: good diquark wins in mass, shows attraction","Static spectator reveals lightest diquark and growing mass gap","Good diquark mass gap widens as quarks get physical","Only 'good' diquark shows attraction, lattice calculation finds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on the assumption that, with an infinitely heavy spectator quark, the correlation function's exponential decay factors cleanly into a diquark mass plus a constant spectator mass, with all $O(m_Q^{-1})$ corrections canceling exactly in mass differences; if those corrections do not cancel, the quoted splittings would mix in other baryon structure.","fun_headline_variants_meta":{"raw":{"variants":["Good diquark stays lightest in lattice QCD with heavy spectator","Lattice QCD: good diquark wins in mass, shows attraction","Static spectator reveals lightest diquark and growing mass gap","Good diquark mass gap widens as quarks get physical","Only 'good' diquark shows attraction, lattice calculation finds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00059,"raw_usage":{"total_tokens":2683,"prompt_tokens":774,"completion_tokens":1909,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":390,"completion_tokens_details":{"reasoning_tokens":1816}},"tokens_in":390,"tokens_out":1909,"duration_ms":14353,"temperature":1.0,"reasoning_tokens":1816,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:32:13.114571+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the bad/good diquark mass splitting on the same gauge ensembles using a different discretization of the static quark (for example, a different smearing or action); if the extracted splitting moves by more than the quoted uncertainties, the $O(m_Q^{-1})$ cancellation assumption is violated. Alternatively, higher-statistics data at the physical pion mass showing the splitting decreasing toward zero, or radial and tangential correlation radii differing in the static case, would contradict the claimed attractive, spherical good diquark.","supporting_citations":[],"review_version":2}