{"id":"edf86d7d-b71a-48cb-91ee-2f787a82512e","arxiv_id":"2501.12863","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Profile-weighted distillation reduces excited-state contamination for static-light and static-charm mesons and yields new spectra and mass splittings on two N_f = 3+1 QCD ensembles.","lead":"This lattice QCD paper shows that an improved version of quark smearing, called optimal distillation profiles, reduces contamination from excited states when computing mesons made of one very heavy and one light quark. It presents new energy spectra for these mesons on two ensembles with pion masses of about 420 and 800 MeV, supporting tests of heavy-quark effective theory and string-breaking.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The improved plateau in Fig. 1 may be due to the GEVP rather than the profile weighting; no standard-distillation GEVP control is shown, so the abstract's attribution to 'optimal profiles' is not isolated.","rationale":"The paper's headline claim is that optimal distillation profiles improve the overlap with energy states relative to standard distillation. This is supported by Fig. 1, which compares improved distillation (7 Gaussian profiles + GEVP) with plain standard distillation on the same ensemble and same N_v=100. The comparison is fair as a practical replacement of one method by another, and the asymptotic masses agree within errors, so the improvement is in the form of reduced excited-state contamination rather than a shifted mass. However, the improved curve combines two elements: profile weighting and a GEVP. The paper does not control for the GEVP step; a GEVP built from multiple standard-distillation operators at different N_v might achieve the same early plateau. If so, the specific attribution to 'optimal profiles' in the abstract and title would be overstated, even though the method itself would still be useful. The reader's weakest assumptions about B*pi contamination and lattice-spacing effects are relevant to the spectroscopic results (Tables 4-5), not to this central methodological claim. I therefore disagree with the reader's identification of the weakest link. The proposed control test on the A1 ensemble would settle the attribution. Since the concern is about the interpretation of a demonstration rather than an internal inconsistency, and since the spectra are new and the limitations are disclosed, the conditional verdict remains appropriate.","tokens_in":7502,"tokens_out":12254,"duration_ms":128087,"concrete_test":"On the A1 ensemble, recompute the static-light ground-state effective mass using a GEVP built from standard distillation correlation functions with seven hard-cutoff operators at N_v = 10, 20, 30, 40, 60, 80, 100 (all subspaces within the first 100 eigenmodes). Compare the plateau onset and fitted mass to the improved-distillation curve in Fig. 1. If the standard-GEVP plateau also starts near t/a=4 with a consistent mass, the improvement is from the GEVP and the central claim's attribution to optimal profiles is not supported; if it remains contaminated like the single-operator curves, the profile shapes are the active ingredient.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that optimal (profile-weighted) distillation improves overlap compared to standard distillation. Figure 1 demonstrates this by comparing improved distillation (7 Gaussian profiles, GEVP) against plain standard distillation (single hard-cutoff operator, no GEVP). Because the improved curve is extracted from a 7x7 GEVP, the earlier plateau and reduced contamination could be a generic variational benefit of the GEVP rather than a property of the profile weighting. The paper does not include a control in which a GEVP is solved using standard-distillation operators at several N_v values (e.g., N_v=10,30,60,100). Without that control, the improvement cannot be uniquely attributed to the optimal profiles; if a standard-distillation GEVP shows the same plateau, the abstract's specific wording overstates the role of the profiles. This matters because the paper's title and abstract emphasize 'optimal distillation profiles' as the innovation.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies improved (profile-weighted) distillation, using Laplacian eigenmodes modulated by Gaussian profiles, to static-light and static-charm mesons on two N_f = 3+1 ensembles with pion masses of about 420 and 800 MeV. Operators are constructed in the relevant fermionic irreps of the doubled cubic group, and a 7-profile GEVP is used to extract energy levels. The central claim is that optimal profiles improve overlap with energy states compared to standard distillation, supported by effective-mass comparisons in Figure 1. The paper also reports S, P1/2 and P3/2 spectra and mass splittings in Tables 4 and 5, compares them with non-interacting B*pi thresholds, and quotes PDG values.","tokens_in":7476,"tokens_out":4471,"duration_ms":47962,"significance":"If the central claim holds, profile-weighted distillation is a practical improvement for heavy-light spectroscopy, and the two-ensemble dataset provides useful static-light and static-charm splittings. The paper deserves credit for the direct same-data comparison in Figure 1, for testing several N_v values for standard distillation, and for openly acknowledging that B*pi operators are missing from the basis. However, the improvement claim is not yet isolated from the GEVP, and the spectroscopic identifications are provisional because scattering-state operators are absent.","major_comments":[{"comment":"The improved-distillation effective mass is extracted from a 7x7 GEVP, while the standard-distillation curves shown in Figure 1 are not reported as GEVP results. The earlier plateau and reduced excited-state contamination of the improved curve could therefore be due to the variational benefit of the GEVP rather than to the profile weighting. To support the abstract and title claim, add a control in which standard hard-cutoff distillation operators are used in a GEVP with comparable basis size (for example N_v = 10, 30, 60, 100), or rephrase the claim as a combined effect of profile weighting plus GEVP.","section":"Section 3, Figure 1"},{"comment":"The levels labeled S, P1/2 and P3/2 are assumed to be single-meson states, but the operator basis contains no B*pi scattering operators. The manuscript itself states at the end of Section 4 that a precise investigation of this contamination requires including B*pi operators. Since the non-interacting B*pi energies lie close to some measured splittings, especially on A1h, the quoted splittings may misidentify scattering states as radial or orbital excitations. The statement that the A1 results \"appear to be more likely radial excitations\" is not a quantitative criterion; the tables should be qualified accordingly, or B*pi operators should be added before assigning these quantum numbers.","section":"Section 4, Tables 4 and 5"},{"comment":"The claimed dependence of the spectrum on the pion mass is not isolated, because the A1 and A1h ensembles differ in lattice spacing (0.05359 fm versus 0.0690 fm) as well as in pion mass. The observed differences in splittings therefore include discretization effects, and without a third ensemble or a continuum extrapolation the differences cannot be uniquely attributed to the light-quark mass. This limitation should be stated explicitly in the discussion of Tables 4 and 5.","section":"Section 4, Figures 3 and 4, and Section 5"}],"minor_comments":[{"comment":"The seven Gaussian profiles used for the GEVP are not specified: neither the functional form nor the shape parameters are given in the text. Please provide the explicit definition or point to the relevant equations in refs. [10, 11].","section":"Section 3"},{"comment":"The PDG entry for the B_s(5840) splitting is garbled; it should read m_{B_s2^*(5840)^0} - m_{B_s^0}. Also, the comparison of the static-light 1P_{3/2} - 1S splitting with both B and B_s PDG values should be commented on, since these states have different light-quark content.","section":"Table 4"},{"comment":"Panel (a) does not identify the standard-distillation curve in the legend; please add the symbol and N_v value used. The caption should also define the shaded bands and state the fit range used for the plateaus.","section":"Figure 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a proceedings contribution and the main technical risk is over-attribution: the improvement shown in Figure 1 is not separated from the GEVP benefit. The B*pi issue is openly acknowledged, but it should be reflected more strongly in the abstract and conclusions. The pion-mass dependence claim should be softened given the different lattice spacings. With a GEVP control and appropriately qualified statements, the paper would be acceptable for the proceedings. I do not see citation or novelty disclosure problems; the method builds on the group's own prior work, which is properly referenced."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the first application of profile-weighted (improved) distillation to static-light and static-charm mesons, with a direct same-data comparison against standard distillation. The effective-mass plot in Figure 1 shows a real practical gain: the improved curve plateaus around t/a = 4, while standard distillation at N_v = 100, 60, 30, and 10 still has contamination. The authors also report new spectra and splittings at two pion masses, and they are admirably explicit about the missing B*pi operators and the need for the G2 irrep. The paper is honest, readable, and a fair status report for LATTICE2024.\n\nHowever, the stress-test note is on target and the reader's take missed it. The improved curve is extracted from a 7x7 GEVP of seven Gaussian profiles; the standard curves are single hard-cutoff operators, no GEVP. There is no control where standard distillation with several N_v values is fed through the same GEVP procedure. So the earlier plateau and reduced contamination could be a generic variational benefit of the GEVP rather than something specifically due to the profile weighting. The abstract states the profiles improve the overlap, and that attribution is not isolated in the data shown. This is a soft spot in the central claim, not a fatal one: the combined method works, but the paper's specific wording overstates what the comparison demonstrates.\n\nTwo more issues, in proportion. First, Table 5 has the static-light 1P3/2 - 1P1/2 splitting jumping from 14.8(7.6) MeV at m_pi ~ 800 to 130(12) MeV at m_pi ~ 420, an order of magnitude above the physical value around 13 MeV. The paper does not discuss this at all, and it is a red flag for the state identification in the P3/2 channel at the lighter pion mass. Second, the pion-mass-dependence conclusion is drawn from two ensembles that differ in lattice spacing as well, so the attribution is not clean. These are limitations, but the authors already disclose the main one (missing B*pi operators).\n\nWho should read this: lattice practitioners working on B-meson spectroscopy, HQET tests, or the group's hybrid string-breaking program, and anyone interested in operator construction. As a proceedings contribution it is fine, but the methodological claim needs a control before I would trust the abstract's wording. My recommendation: send it to peer review, and ask the authors to add a standard-distillation GEVP control, report fit ranges, and address the anomalous splitting. The work deserves referee time, but with revision.","headline":"Useful application of profile-weighted distillation to static-light mesons, but the abstract's claim that the 'optimal profiles' are what improves overlap is not actually isolated from the GEVP benefit, and one splitting in Table 5 looks anomalous.","tokens_in":8247,"tokens_out":1686,"would_cite":true,"duration_ms":18630,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Gc"],"model":"deepseek-v4-flash","headline":"A profile-weighted variant of lattice distillation suppresses excited-state contamination in static-light and static-charm meson correlation functions, producing cleaner effective-mass plateaus and S, P1/2, and P3/2 mass splittings at two…","keywords":["static-light mesons","lattice QCD","optimal distillation profiles","heavy quark effective theory","excited-state contamination","mass splittings","generalized eigenvalue problem","B*pi states"],"falsifier":"Extend the GEVP basis on the A1 ensemble with $B^*\\pi$ interpolating operators (pion momenta zero and one unit) and recompute the static-light spectrum. If the level quoted as $1P_{1/2}$ at $277.9(6.9)$ MeV above the ground state, or the $1P_{3/2}$ level at $408(10)$ MeV, shifts by more than the quoted error, or a third level appears below the quoted $2S$ state, then the single-meson labels in Tables 4 and 5 are falsified.","tokens_in":7112,"feed_emoji":"⚛️","tokens_out":12004,"duration_ms":107935,"temperature":0.7,"pith_summary":"This paper aims to establish that \"optimal distillation profiles\"—a profile function that weights the eigenmodes of the 3D gauge-covariant Laplacian in lattice-QCD smearing—improve the overlap with energy eigenstates for static-light and static-charm mesons compared with standard distillation. On the $m_\\pi \\approx 420\\,\\mathrm{MeV}$ ensemble, the improved method gives an effective ground-state mass of $a m = 0.30594(81)$ with a plateau that begins near $t/a = 4$, while standard distillation at the same eigenvector count still shows excited-state contamination ($a m = 0.30773(87)$). The same technique is used to extract S, P1/2, and P3/2 spectra and mass splittings at pion masses of about 420 and 800 MeV. If correct, the method provides a cleaner route to heavy-light spectroscopy and tests of heavy-quark effective theory, with a static-light spectrum that responds more strongly to the light-quark mass than the static-charm spectrum.","feed_headline":"Optimal profiles reduce excited-state noise in static-light mesons","feed_subtitle":"Profile-weighted smearing gives a plateau from t/a=4 and new S, P1/2, P3/2 splittings at two pion masses.","key_machinery":"The central object is the optimal distillation profile $\\rho_i(t) = \\rho(\\lambda_i(t))$, a function of the eigenvalues $\\lambda_i$ of the 3D gauge-covariant Laplacian that modulates each eigenvector's weight in the smeared quark field; standard distillation is the special case of a step-function profile that keeps only the $N_v$ lowest modes. Using $N = 7$ Gaussian profiles builds an $N \\times N$ correlation matrix whose energy levels are extracted with the generalized eigenvalue problem (GEVP), the machinery of [13,14]. The profile functions are what suppress excited-state contamination, and the local plus derivative operators, projected onto fermionic irreducible representations of the doubled cubic group, provide access to the S, $P_{1/2}$, and $P_{3/2}$ channels.","core_discovery":"The central claim, stated in the abstract, is that the use of optimal profiles improves the overlap with the energy states compared to standard distillation. Concretely, Figure 1 compares the static-light ground-state effective mass on the A1 ensemble: with $N_v = 100$ Laplacian eigenvectors, standard distillation yields $a m = 0.30773(87)$ with visible excited-state contamination, while improved distillation with seven Gaussian profiles yields $a m = 0.30594(81)$ and a plateau from about $t/a = 4$. The paper then applies the improved technique to measure the static-light and static-charm spectra in the $G_1^+$, $G_1^-$, and $H^-$ irreps, identified with continuum $S$, $P_{1/2}$, and $P_{3/2}$ states, and reports mass splittings (Tables 4 and 5) at two pion masses. Non-interacting $B^*\\pi$ energies are included for comparison, and the authors state that a precise investigation of $B^*\\pi$ excited-state contamination would require adding $B^*\\pi$ operators to the basis. It also concludes that static-light meson splittings depend more strongly on the pion mass than static-charm splittings, which largely cancel the heavy-quark mass dependence when the ground-state mass is subtracted.","pith_inferences":["Beyond the paper, if the profile improvement persists at the physical pion mass and with more eigenmodes, optimal-profile distillation could reduce the need to construct explicit multi-particle interpolators for the lower heavy-light spectrum, since the profiles automatically emphasize the relevant wavefunction components.","Because the A1 and A1h ensembles differ in lattice spacing as well as pion mass, the attributed pion-mass dependence of the static-light splittings, such as $1P_{1/2}-1S$ changing from $277.9(6.9)$ to $369.9(5.6)$ MeV, is not isolated from discretization effects; a comparison at fixed lattice spacing would separate the two.","The planned $H$/$G_2$ comparison for the putative $5/2$ state doubles as a lattice-artifact test: if the two irreps that should form the continuum $5/2$ level do not align, the $P_{3/2}$ assignments carry residual symmetry-breaking contamination.","If the $B^*\\pi$ check leaves the A1 excited levels unchanged, the first excited states in the $G_1^-$ and $H^-$ channels are predominantly single-meson radial excitations, which would make them usable inputs for heavy-meson chiral perturbation theory."],"forward_implications":["Using the same number of Laplacian eigenvectors, optimal profiles give a longer, cleaner plateau than standard distillation, so static-light and static-charm ground-state masses can be extracted with smaller systematic error.","The improved method makes higher radial and orbital excitations (2S, P1/2, P3/2) accessible enough that splittings such as $1P_{1/2}-1S$, $1P_{3/2}-1S$, and $2S-1S$ can be quoted at two pion masses.","The static-light splittings quoted on the $m_\\pi \\approx 420$ MeV ensemble, for example $1P_{3/2}-1S = 408(10)$ MeV, are the values the authors put forward for comparison with experimental B-meson splittings after extrapolation to the physical pion mass.","The heavier-pion A1h result shows $B^*\\pi$ energies closer to the measured levels than the A1 result, so the paper's proposed next step of adding $B^*\\pi$ operators is needed before any level can be labeled unambiguously as a meson excitation rather than a scattering state."],"supporting_citations":[{"why":"Introduces the optimal meson distillation profile technique that the paper applies to static-light and static-charm systems.","marker":"[10]"},{"why":"Constructs static quark creation operators from Laplacian eigenmodes, providing the profile construction for static quarks.","marker":"[11]"},{"why":"Defines standard distillation, the smearing method whose hard eigenmode truncation is improved here.","marker":"[12]"},{"why":"Introduces the generalized eigenvalue problem used to extract energy levels from the profile-weighted correlation matrix.","marker":"[13]"},{"why":"Extends the GEVP method to energy and matrix-element extraction in lattice field theory, justifying the level determination.","marker":"[14]"},{"why":"Supplies the $N_f = 3+1$ ensemble action and parameters used for the A1 and A1h runs.","marker":"[15]"},{"why":"Gives the subduction of continuum angular-momentum states to lattice irreps and the spectral notation used for static-light mesons.","marker":"[5]"},{"why":"Provides the experimental B and $B_c$ meson splittings used for comparison in Table 4.","marker":"[17]"}],"fun_headline_variants":["Optimal distillation profiles improve static-light meson overlap","Gaussian profiles yield cleaner static-light spectra than standard distillation","Static-light spectroscopy: optimized profiles beat standard distillation","New static-light and static-charm splittings with optimal smearing","Plateau from t/a=4 via optimal profiles in static-light mesons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that each level extracted from the GEVP basis is an S, P1/2, or P3/2 single-meson state, even though the basis contains no $B^*\\pi$ two-particle operators; if one of the extracted levels is actually a $B^*\\pi$ scattering state, the corresponding splitting in Tables 4 and 5 mislabels a meson state.","fun_headline_variants_meta":{"raw":{"variants":["Optimal distillation profiles improve static-light meson overlap","Gaussian profiles yield cleaner static-light spectra than standard distillation","Static-light spectroscopy: optimized profiles beat standard distillation","New static-light and static-charm splittings with optimal smearing","Plateau from t/a=4 via optimal profiles in static-light mesons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000279,"raw_usage":{"total_tokens":1643,"prompt_tokens":917,"completion_tokens":726,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":533,"completion_tokens_details":{"reasoning_tokens":642}},"tokens_in":533,"tokens_out":726,"duration_ms":6364,"temperature":1.0,"reasoning_tokens":642,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:47:44.785154+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Extend the GEVP basis on the A1 ensemble with $B^*\\pi$ interpolating operators (pion momenta zero and one unit) and recompute the static-light spectrum. If the level quoted as $1P_{1/2}$ at $277.9(6.9)$ MeV above the ground state, or the $1P_{3/2}$ level at $408(10)$ MeV, shifts by more than the quoted error, or a third level appears below the quoted $2S$ state, then the single-meson labels in Tables 4 and 5 are falsified.","supporting_citations":[{"cited_title":"Radial and orbital excitations of static-light mesons","cited_arxiv_id":"hep-lat/0702010","evidence_quote":"Gives the subduction of continuum angular-momentum states to lattice irreps and the spectral notation used for static-light mesons."},{"cited_title":"Navas et al.,Review of particle physics, Phys","cited_arxiv_id":null,"evidence_quote":"Provides the experimental B and $B_c$ meson splittings used for comparison in Table 4."}],"review_version":1}