{"id":"e5ad5dba-8973-4130-bf11-9199477636a1","arxiv_id":"2501.02839","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The 2830 MeV excess in LHCb B+ -> D*- D_s+ pi+ data is consistent with the predicted J=2 tetraquark T_cs2, with angular moments proposed to confirm the spin.","lead":"This paper re-fits LHCb data on B+ -> D*- D_s+ pi+ decays, where an unexplained bump appears around 2830 MeV. It argues the bump could be the predicted spin-2 tetraquark T_cs2 and computes angular moments that could help identify its spin.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central evidence rests on an unquantified visual excess at 2830 MeV: the fit fixes the resonance mass and width to theory, reports no significance or no-resonance comparison, and all three spin hypotheses match the same 1D spectrum.","rationale":"Reading the paper in good faith, it is a compact phenomenological follow-up applying a standard angular-momentum formalism. The moment formulas in Eqs. (1)-(9) are internally consistent with the Clebsch-Gordan relation in Eq. (6), and no mathematical error jumps out. The fit procedure is clear but minimal. The load-bearing point is exactly the one the reader identified: the existence of the 2830 MeV structure is assumed, not demonstrated. The paper supplies no significance estimate, no comparison to a background-only fit, and no fit-quality metric; because M_R and Gamma_R are fixed from Ref. [30], the agreement at 2830 MeV cannot be scored as an independent prediction. All three spin cases reproduce the same one-dimensional mass distribution within the quoted qualitative agreement, so the data cannot currently distinguish J = 0, 1, or 2, and the moments are predictions contingent on an unconfirmed resonance. The strongest positive feature is the proposal to measure angular moments as a future spin discriminator; that part is useful and can survive in a properly conditioned version. The title and the Sec. IV phrasing ('evidence', 'strong support') outrun the quantitative support. No internal inconsistency requires rejection; the appropriate outcome is the reader's CONDITIONAL verdict with the requested softening, significance quantification, and background justification.","tokens_in":8952,"tokens_out":4682,"duration_ms":54411,"concrete_test":"Digitize the efficiency-corrected D_s+ pi+ invariant-mass yields in Fig. 9(b) of Ref. [39] over 2650-3150 MeV and perform a binned Poisson likelihood fit under two hypotheses: (H0) a smooth non-resonant background, e.g. B(M) proportional to p_D* k with shape parameters analogous to Eq. (13) plus optional low-order polynomial terms, and (H1) H0 plus a Breit-Wigner with M_R and Gamma_R floated near the predicted 2834 MeV. Compute 2 Delta ln L and a p-value with an appropriate look-elsewhere factor. Also fit the three spin cases with M_R and Gamma_R floated and compare their goodness of fit. If H1 does not improve the likelihood at p < 10^-2 after the trials factor, or if the J = 0, 1, 2 fits differ by less than the statistical resolution in Delta chi^2, the title-level evidence claim should be withdrawn and the paper reframed as a proposal for future moment measurements.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the LHCb data give 'strong support' to T_cs2 rests on a premise the paper never establishes: that the event excess near 2.83 GeV in Fig. 9(b) of Ref. [39] is a genuine resonance. LHCb did not identify a state there, and the paper quotes no significance, no fit probability, and no comparison against a non-resonant hypothesis. The fits in Sec. III are constructed with the pole position fixed to theory, M_R = 2834 MeV and Gamma_R = 19 MeV from Ref. [30], stated just before Eqs. (10)-(12), so agreement with data at 2830 MeV is partly built in and cannot serve as independent confirmation. With only two fitted coefficients per case plus the ad hoc background replacement a_i -> a~_i k/M_B in Eq. (13), the model can accommodate a modest enhancement; no Delta chi^2 between cases or relative to a no-resonance fit is shown. Indeed, Figs. 3-5 show that the angular-integrated spectrum is described comparably for J = 0, 1, and 2, so this observable cannot by itself establish the resonance, let alone its spin. The predicted moments of Eq. (7) are conditional predictions: they are evaluations of fitted amplitudes, not measurements, and would only become evidence if the resonance hypothesis is first confirmed. The Sec. IV appeal to a similar bump in B+ -> D*-D+K+ is suggestive but again cites a structure not established as a resonance in that analysis; two unquantified bumps do not by themselves make a Breit-Wigner. If the excess is a statistical fluctuation, a kinematic reflection, or a background artifact, the identification with T_cs2 collapses.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript analyzes the D_s^+π^+ invariant mass spectrum of the LHCb process B^+ → D^{*-}D_s^+π^+ and argues that a broad excess near 2830 MeV is the predicted J^P=2^+ tetraquark T_cs2, the spin partner of T_cs0(2900). The authors use a compact amplitude with an S-wave background plus a resonance term, fixing the resonance mass and width to the theoretical values M_R=2834 MeV and Γ_R=19 MeV from Ref. [30]. They fit two coefficients per spin hypothesis (J=0,1,2), compare the angular-integrated dΓ/dM_inv with LHCb data, and compute angular moments dΓ_l/dM_inv for l=0–4, finding that the moments differ markedly between the spin assignments. The paper concludes that the data give 'strong support' to the T_cs2 interpretation and calls for an experimental measurement of the moments.","tokens_in":9342,"tokens_out":6254,"duration_ms":61513,"significance":"The paper's positive contribution is to work out the angular-moment decomposition for the three spin hypotheses and to show, with a simple amplitude model, that these moments are sensitive to the spin of a possible resonance. It also takes the pole parameters from an independent coupled-channel prediction, which avoids fitting mass and width to the data. If the 2830 MeV excess is established as a genuine resonance, the predicted moments would provide a concrete test of the T_cs2 interpretation. The authors honestly note that the angular-integrated spectrum alone cannot distinguish the spins. The central limitation is that the manuscript does not quantify the statistical evidence for the excess, so the claim of 'evidence' is stronger than the analysis currently supports.","major_comments":[{"comment":"The fits fix the resonance mass and width to the theoretical values M_R=2834 MeV and Γ_R=19 MeV from Ref. [30], and no fit-quality metric is reported: there is no χ²/ndof, no Δχ² relative to a no-resonance or alternative-background fit, and no estimate of the statistical significance of the 2830 MeV excess. Because the title and Sec. IV conclude that the LHCb data give 'strong support' for T_cs2, the analysis must demonstrate quantitatively that the excess is not a statistical fluctuation or background artifact; currently the agreement is only stated as 'fair agreement' without quantitative support.","section":"Sec. III, Eqs. (10)–(12) and Figs. 3–5"},{"comment":"The angular moments dΓ_l/dM_inv are evaluated after fitting the coefficients (a0, a'0), (a1, c'), or (a2, b') to the same angular-integrated LHCb distribution. Therefore the moments are algebraically determined by the fitted amplitudes rather than being independent predictions; they can discriminate spin only if the resonance and background model are already assumed correct. The paper should explicitly describe these moments as conditional evaluations under the assumed model, not as predictions that can by themselves confirm the existence of T_cs2.","section":"Sec. II, Eq. (7) and Sec. III, Eqs. (10)–(12)"},{"comment":"The empirical basis for the claimed 2.83 GeV structure is a visual event excess in Fig. 9(b) of Ref. [39]; LHCb did not identify a resonance at this mass, and the present paper quotes no significance or compatibility test. The statement in Sec. IV that the same energy appearing in both B^+ → D^{*-}D^+K^+ and B^+ → D^{*-}D_s^+π^+ gives 'strong support' presupposes that both peaks are genuine resonances, which is exactly what needs to be established. The paper should either derive a local significance from the binned distribution or visibly temper this conclusion.","section":"Sec. I and Sec. IV"},{"comment":"The background model ai → ãi k/M_B is introduced ad hoc, with no justification and no uncertainty. With only two fitted parameters per case and this flexible background, the fit can absorb smooth enhancements, so the apparent agreement with the data does not by itself validate the resonance hypothesis. The authors should motivate the background shape and show that the fitted resonance parameters are stable under plausible variations of the background model.","section":"Sec. III, Eq. (13)"}],"minor_comments":[{"comment":"The terms 'momenta of the angular mass distribution' and 'momentum magnitude' should be 'moments' and 'moment magnitude'; angular moments are meant, not momenta of particles.","section":"Abstract and Sec. II"},{"comment":"The sentence introducing 'the term of bY20' to account for a J^P=1^- state coupling in P-wave is inconsistent with the amplitude decomposition, since bY20 is a D-wave (l=2) term; the P-wave piece is cY10. Please clarify the intended wording.","section":"Sec. II, text after Eq. (1)"},{"comment":"The choice of the fit window 2650–3150 MeV is not justified; the authors should state why this range is selected and whether the conclusions depend on the window boundaries.","section":"Sec. III, fit range"},{"comment":"The plotted dΓ_l/dM_inv moments are in arbitrary units; the paper should specify how future experimental moments should be normalized to allow a quantitative comparison.","section":"Sec. III, figures"},{"comment":"The conclusion that a structure at 2830 MeV appears in two different final states would be strengthened by quoting the relevant mass and width values from Ref. [36] and by discussing the compatibility of the two measurements, rather than only noting the same energy.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The paper is a phenomenological analysis that could be publishable after a major revision that adds quantitative significance, propagated uncertainties, and tempered language. The central claim of 'evidence' currently rests on an unquantified visual excess, so I would not support acceptance in the present form. The manuscript relies heavily on the authors' own previous work for the model framework; this is not inappropriate in this subfield, but independent validation would strengthen the argument."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper applies an existing angular-moment analysis to a new channel, B+ -> D*- D_s+ pi+, and that is a perfectly fine thing to do. But the title says \"Evidence\" and that oversells it. There is no quantitative evidence yet, and the analysis as written cannot support the strong claim in Sec. IV.\n\nWhat is actually new: the moments dGamma_1 through dGamma_4 for this channel under the J=0,1,2 hypotheses, and the honest statement that the angular-integrated spectrum alone cannot separate the spins. That last point is useful. The moment calculation is straightforward and the Legendre relations in Eq. (7) look right. The call for LHCb to measure these moments is concrete and testable.\n\nThe soft spots are real and partly load-bearing. First, the 2830 MeV excess in the LHCb data is treated as a resonance without quoting a significance, a fit probability, or a comparison against a non-resonant background. LHCb did not claim a state there. Second, the fits fix M_R = 2834 MeV and Gamma_R = 19 MeV from theory, so the agreement at 2830 MeV is partly built in. Third, no uncertainties or chi-square values are reported for the fitted coefficients, and the background replacement a_i -> tilde a_i k/M_B is ad hoc. Fourth, the advertised moments are conditional predictions: they are evaluations using the same coefficients fitted to the same data, so they are not independent confirmations of the resonance. Finally, the \"strong support\" argument from B+ -> D*-D+K+ is weak because that 2830 MeV peak is likewise not established as a resonance in the cited analysis; two unquantified bumps do not make a Breit-Wigner.\n\nI do not think the paper is wrong in its proposal. Measuring the moments is a good idea, and the formalism is sound. But the title and conclusion overclaim. With significance, fit quality, and a no-resonance comparison, this could be a solid experimental proposal. As is, I would send it to a referee because the formalism is sound and the experimental ask is concrete, though I would expect major revision. If the excess is a fluctuation, the whole identification collapses.","headline":"A useful and testable angular-moment proposal for the new LHCb channel, but the title-level claim of evidence is not supported by the analysis: no significance, no fit quality, and the resonance parameters are fixed to theory.","tokens_in":9915,"tokens_out":2778,"would_cite":false,"duration_ms":28721,"reading_group":"maybe","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 argues that a resonant-like structure near 2830 MeV in the D_s+ π+ mass distribution of B+ → D*- D_s+ π+, measured by LHCb, is the predicted open-flavor tetraquark T_cs2, the spin J=2 partner of T_cs0(2900).","keywords":["open-flavor tetraquark","T_cs0(2900)","T_cs2","spin partner","angular moments","B meson decay","exotic hadron"],"falsifier":"A measurement of the moments in B+ → D*- D_s+ π+ that does not show the predicted J=2 pattern—for example, no dΓ4/dM signal or dΓ2 not exceeding dΓ0 near 2830 MeV—would rule out the T_cs2 interpretation, as would a higher-statistics analysis showing that the 2830 MeV excess disappears with improved background modeling.","tokens_in":8724,"feed_emoji":"⚛️","tokens_out":4686,"duration_ms":42526,"temperature":0.7,"pith_summary":"The paper claims that the excess of events around 2830 MeV in the D_s+ π+ invariant mass distribution of B+ → D*- D_s+ π+, measured by LHCb, corresponds to the predicted open-flavor tetraquark T_cs2, the spin J=2 partner of T_cs0(2900). The authors show that the angular-integrated mass spectrum can be fitted equally well by J=0, 1, or 2 resonances, so the mass distribution alone cannot fix the spin. They then compute angular moments (projections onto spherical harmonics) from l=0 to 4 and show that each spin assumption gives a drastically different pattern. For the favored J=2 case, the interference moment dΓ2/dM is predicted to have larger strength at the resonant energy than the angle-integrated signal, providing a clear experimental target. The paper concludes that the coincidence of a 2830 MeV peak in both B+ → D*- D+K+ and B+ → D*- D_s+ π+ strongly supports identifying the structure as T_cs2, and urges experimental determination of these moments.","feed_headline":"Bump at 2830 MeV points to T_cs2 tetraquark","feed_subtitle":"Angular moments of the D_s+ pi+ distribution separate spin 2 from spin 0 and 1.","key_machinery":"The central object is the amplitude T = ε_μ(D*−) P^μ_{B+} (a Y00 + b Y20 + c Y10), where a, b, c represent S-wave, D-wave, and P-wave resonance contributions and Y_l0 are spherical harmonics. This yields explicit expressions for the angular moments dΓ_l/dM in terms of |a|², |b|², |c|² and their interferences, so that measuring a few moments fixes which partial wave (and hence spin) is present. The resonance parameters are taken from the predicted T_cs2: M_R = 2834 MeV and Γ_R = 19 MeV.","core_discovery":"On the paper's own terms, the D_s+ π+ mass distribution from LHCb shows an event excess near 2830 MeV that the existing fit cannot describe. Adopting the prediction that the J^P = 2+ partner of T_cs0(2900) has mass 2834 MeV and width 19 MeV, the authors write the production amplitude for B+ → D*- D_s+ π+ as a tree-level term plus a resonance term in S-wave, P-wave, or D-wave, fit the free parameters to the LHCb data, and find all three fits succeed. They then decompose the squared amplitude into moments dΓ_l/dM (l = 0,...,4) using spherical harmonics. Each spin assumption yields a distinct pattern: J=0 contributes only dΓ0, J=1 contributes dΓ0, dΓ1, and dΓ2, and J=2 contributes dΓ0, dΓ2, and dΓ4. Since the angle-integrated spectrum cannot distinguish these cases, the moments are the discriminating observable; for the preferred J=2 case the dΓ2 moment is predicted to exceed the angle-integrated signal near the peak.","pith_inferences":["The paper assumes the 2830 MeV excess in B+ → D*- D_s+ π+ is the same object as the 2830 MeV peak in B+ → D*- D+K+; a combined simultaneous fit of both reactions could test whether the two peaks share one Breit-Wigner pole.","The predicted moments assume the resonance mass and width are fixed at 2834 MeV and 19 MeV; a scan over M_R and Γ_R would show whether the discriminating power of the moments survives off-prediction values.","Because the background parameters are refit for each spin case, part of the moment differences could be absorbed by different background shapes; dedicated amplitude analyses with full background uncertainty models would sharpen the spin discrimination.","The moment-decomposition technique could be extended to other predicted spin partners of open-flavor tetraquarks in different B-decay channels."],"forward_implications":["If LHCb measures the moments of the D_s+ π+ distribution, a nonzero dΓ4/dM with dΓ2 stronger than dΓ0 near 2830 MeV would establish the J=2 assignment and confirm T_cs2.","The same moment analysis can be applied to the similar 2830 MeV peak in B+ → D*- D+K+, providing a cross-check of the resonance's spin.","A confirmed J=2 partner would support the coupled-channel molecular interpretation of T_cs0(2900), in which the state emerges from D*K* and D*_s ρ interactions.","The method offers a template for identifying the spin of exotic-state candidates in other three-body B decays."],"supporting_citations":[{"why":"Predicts the T_cs2 state with mass 2834 MeV and width 19 MeV, providing the resonance parameters used in the fits.","marker":"[30]"},{"why":"Provides the LHCb data for B+ → D*- D_s+ π+ and the 2830 MeV excess that is the subject of the analysis.","marker":"[39]"},{"why":"Shows the 2830 MeV peak in B+ → D*- D+K+ that the paper uses as corroborating evidence for the same resonance.","marker":"[36]"},{"why":"Earlier study by the same group finding the 2830 MeV peak in B+ → D*- D+K+ could be the T_cs2; the present work extends this analysis to the D_s+ π+ channel.","marker":"[37]"},{"why":"Predicts a T_cs2 state with mass around 2800 MeV, supporting the mass region of the observed excess.","marker":"[26]"},{"why":"Predicted the spin partners of the X0(2900) family, establishing the framework in which T_cs2 is a J=2 partner of T_cs0(2900).","marker":"[35]"}],"fun_headline_variants":["LHCb bump hints at spin-2 tetraquark partner","Angular moments point to T_cs2 tetraquark","2830 MeV excess matches predicted T_cs2","Spin-2 partner of T_cs0(2900) may be seen"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The excess of events around 2830 MeV in the LHCb data is a genuine resonance rather than a statistical fluctuation, a kinematic reflection, or a background artifact; LHCb itself did not identify a resonance at this mass.","fun_headline_variants_meta":{"raw":{"variants":["LHCb bump hints at spin-2 tetraquark partner","Angular moments point to T_cs2 tetraquark","2830 MeV excess matches predicted T_cs2","Spin-2 partner of T_cs0(2900) may be seen"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000264,"raw_usage":{"total_tokens":1634,"prompt_tokens":1005,"completion_tokens":629,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":621,"completion_tokens_details":{"reasoning_tokens":555}},"tokens_in":621,"tokens_out":629,"duration_ms":6722,"temperature":1.0,"reasoning_tokens":555,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:01:46.632683+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A measurement of the moments in B+ → D*- D_s+ π+ that does not show the predicted J=2 pattern—for example, no dΓ4/dM signal or dΓ2 not exceeding dΓ0 near 2830 MeV—would rule out the T_cs2 interpretation, as would a higher-statistics analysis showing that the 2830 MeV excess disappears with improved background modeling.","supporting_citations":[{"cited_title":"Molina and E","cited_arxiv_id":null,"evidence_quote":"Predicts the T_cs2 state with mass 2834 MeV and width 19 MeV, providing the resonance parameters used in the fits."},{"cited_title":"Aaij et al","cited_arxiv_id":null,"evidence_quote":"Provides the LHCb data for B+ → D*- D_s+ π+ and the 2830 MeV excess that is the subject of the analysis."},{"cited_title":"Aaij et al.[LHCb], Phys","cited_arxiv_id":null,"evidence_quote":"Shows the 2830 MeV peak in B+ → D*- D+K+ that the paper uses as corroborating evidence for the same resonance."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier study by the same group finding the 2830 MeV peak in B+ → D*- D+K+ could be the T_cs2; the present work extends this analysis to the D_s+ π+ channel."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts a T_cs2 state with mass around 2800 MeV, supporting the mass region of the observed excess."},{"cited_title":"Molina, T","cited_arxiv_id":null,"evidence_quote":"Predicted the spin partners of the X0(2900) family, establishing the framework in which T_cs2 is a J=2 partner of T_cs0(2900)."}],"review_version":1}