{"id":"15f55d17-cc40-4b65-ac02-b576580e6c61","arxiv_id":"2601.01382","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"A molecular-model fit to Belle II data gives a (9.7±3.9)% Tcs0(2900)^0 fit fraction in B−→K−D0K0, proposing a clean probe of the state.","lead":"This paper estimates that the exotic four-quark candidate Tcs0(2900)^0 should show up with a roughly 10% fit fraction in B−→K−D0K0, a decay it argues is cleaner than previously studied channels. If the signal is confirmed at Belle II or LHCb, it would help decide whether Tcs0(2900) is a D*K* molecule or something else.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Signal significance and molecular discrimination are not established: a4 is free and no no-Tcs fit is shown; a compact tetraquark would give a similar BW peak.","rationale":"The paper's strongest claim has two parts: that the molecular Tcs contributes significantly in B−→K−D0K0, and that this channel can establish the molecular component and discriminate it from a compact tetraquark. Both parts rest on the fit in 'Numerical results.' Because a4 is free, the signal strength is not predicted from the molecular hypothesis; the fit fraction is an output, not a test. Without a no-signal fit, we do not know whether the Tcs term is necessary at all. Even if it is necessary, the only molecular-specific input is the loop function G in the amplitude; a compact tetraquark would appear as a similar Breit-Wigner peak, and the paper does not quantify how much the G factor distorts the line shape over the 119 MeV width. These omissions are addressable with a likelihood-ratio test, which is why the concern does not force rejection. The reader's CONDITIONAL verdict already captures the need for additional evidence, so I recommend retaining it.","tokens_in":9006,"tokens_out":10978,"duration_ms":122668,"concrete_test":"Perform a likelihood-ratio test on the Belle II data of Ref. [37] by refitting the model of the 'Numerical results' section with (i) a4 fixed to 0 and (ii) a pure Breit-Wigner instead of the loop-modified amplitude, each with a flat nonresonant D0K0 term; report Δχ² relative to the nominal fit. If Δχ²(i) < 9, the Tcs term is not statistically required; if Δχ²(ii) versus the nominal molecular fit is < 4, the data cannot discriminate molecular from compact line shapes.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The fit in 'Numerical results' uses t_T = a4 · G · g_{D*K*}·g_{DK}/(M^2 - m_T^2 + i m_T Γ_T) (Eq. 11), with a4 a free parameter. Thus the molecular model fixes only the line shape, not the rate; the quoted fit fraction R=(9.72±3.92)% is a fit output, not a prediction of the molecular hypothesis. The paper does not report a fit with a4=0 or with a pure Breit-Wigner replacing the loop-modified line shape, so it does not establish that the Tcs term is statistically required, nor that the data prefer the molecular line shape over a compact-tetraquark BW. A compact tetraquark with the same J^P=0^+, mass 2892 MeV, and width 119 MeV would produce an almost identical peak in D0K0; the analysis as presented cannot discriminate between the two interpretations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes B−→K−D0K0 as a clean channel to search for the neutral T_cλs0(2900)^0 in the D*K* molecular picture. The authors construct an amplitude containing a T_cλs0(2900)^0 contribution with a loop-modified Breit-Wigner shape, together with ρ(770), ρ(1450), and a0(980) contributions, and fit the Belle II invariant mass distributions for K−K0, D0K0, and D0K−. They report a good fit (χ²/d.o.f. = 1.07) and a T_cλs0(2900)^0 fit fraction R = (9.72±3.92)%, arguing that this establishes a significant molecular component and that the channel can help distinguish molecular from compact-tetraquark interpretations.","tokens_in":9303,"tokens_out":6325,"duration_ms":67904,"significance":"If the molecular interpretation and the quantitative claim were robust, this would be a valuable contribution: the channel B−→K−D0K0 is indeed cleaner than previously considered final states, with no charmonium or isoscalar X0,1(2900) background, and the fit achieves a good description of three measured spectra. The paper also incorporates the K* width via a convolution, which is a physically sensible refinement. However, the central quantitative claim is weakened by the fact that the T_cλs0 amplitude normalization is a free fit parameter, and the analysis does not yet demonstrate that the data require the T_cλs0 term or prefer the molecular line shape over a compact-tetraquark Breit-Wigner. The strengths are the clear identification of a promising experimental channel and a reasonable phenomenological model for the background resonances.","major_comments":[{"comment":"The T_cλs0(2900)^0 amplitude in Eq. (11) contains the free parameter a4, which is fitted to the same Belle II D0K0 distribution that the paper then claims the T_cλs0 state explains. Consequently the quoted fit fraction R=(9.72±3.92)% is an output of the fit, not a prediction of the molecular model. To support the central claim, the authors should report the fit without the T_cλs0 term (a4=0) and give the change in χ² or a likelihood-ratio test. Without this, the statement that T_cλs0 is 'essential for describing the D0K0 invariant mass distribution' is not established.","section":"Numerical results, Eq. (11), Table I"},{"comment":"The paper claims that the analysis can help clarify the nature of T_cλs0(2900) and discriminate between molecular and compact-tetraquark interpretations, but no such discrimination is demonstrated. The T_cλs0 line shape in Eq. (11) is a loop-modified Breit-Wigner with a free normalization; a compact tetraquark of the same mass, width and J^P=0^+ would produce a nearly identical Breit-Wigner peak in D0K0. The authors should fit the data with a pure Breit-Wigner for the T_cλs0 signal and compare the fit quality or the extracted parameters. In the present form, the data description cannot distinguish the two scenarios.","section":"Summary and numerical results"},{"comment":"No nonresonant background is included in the amplitude. The fit includes only resonant contributions (ρ, ρ′, a0, T_cλs0), but B-decay Dalitz plots typically contain a smooth nonresonant component. If such a component is present, the fitted a4 (and therefore the T_cλs0 fit fraction) may absorb part of the background. The authors should test the stability of R by adding a constant or phase-space-motivated nonresonant amplitude to the fit, or explicitly justify its omission.","section":"Model, Eq. (3) and numerical results"},{"comment":"The quoted uncertainty on R, stated to arise from the fitting error of a4 and the experimental uncertainty in B(B−→K−D0K0), omits important model dependences. In particular, the assumed branching fraction B(T_cλs0→D0K0)=65% (from Ref. [11], which gives 60–70%), the loop parameters α and μ, the compositeness parameter λ̃, and the K* width smearing all enter the T_cλs0 amplitude or coupling and are not varied. The uncertainty on R is therefore likely underestimated. The authors should propagate these model uncertainties or at least show the sensitivity of R to the B=60–70% range and to reasonable variations of α and μ.","section":"Uncertainties, Eq. (8), Eq. (9)"}],"minor_comments":[{"comment":"The sentence 'The function G(MD0K0, mD0, mK0) is the two-meson loop integral for the D0K0 intermediate state' appears to be a typo: the arguments in Eq. (2) are (M_D0K0, m_D*0, m_K*0), and the loop is for the D*K* intermediate state, not D0K0.","section":"Eq. (2) and surrounding text"},{"comment":"The reduced mass μ is defined as m_D0 m_K0/(m_D*0 + m_K*0), but for a D*K* molecular state one would expect μ = m_D*0 m_K*0/(m_D*0 + m_K*0). Please clarify why the D0 and K0 masses are used in the compositeness condition rather than the constituent D* and K* masses.","section":"Eq. (8)"},{"comment":"The purple curves in panels (a) and (c) are described as the projection of the T_cλs0 contribution, but the curve in panel (a) appears nearly flat and close to zero in the plotted range. This is plausible given the Dalitz projection, but a brief explanation or a logarithmic inset would help the reader see what the T_cλs0 contribution actually does in K−K0 and D0K− spectra.","section":"Fig. 4"},{"comment":"The parameters a1, a2, a3 and a4 have different dimensions, but the table gives no units or indication of the dimension of each coefficient. Adding a column with units (or stating that the ai are in GeV with the appropriate power) would improve readability.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"The paper's central claim is a prediction of a significant T_cλs0(2900)^0 signal in B−→K−D0K0, but as presented the signal normalization is fitted to the very data it is supposed to explain. The lack of a no-signal fit and of a comparison with a compact-tetraquark line shape are the main obstacles. I believe these issues are addressable within the scope of the manuscript: the authors can add a baseline fit without T_cλs0, compare pure Breit-Wigner and loop-modified shapes, and expand the error budget. I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the channel choice is sensible and worth pursuing, but the central quantitative claim — a (9.72±3.92)% fit fraction — is not a prediction of the molecular model. It is a fit output controlled by the free parameter a4, fitted to the very Belle II D0K0 distribution the paper says it explains. The paper never shows a fit with a4=0, so we don't know if the Tcs0 peak is statistically required.\n\nWhat is genuinely new: the use of B−→K−D0K0 as a clean probe. The arguments for cleanliness — no charmonium states, no X0,1(2900), only isovector contributions — are sound. The fit to the Belle II spectra looks reasonable (χ2/dof=1.07), and the authors are transparent about listing a4 as a free parameter. The machinery (compositeness, loop functions, spectral convolution) is standard and not mishandled in any obvious way.\n\nThe soft spots are the ones you'd expect. First, the 'estimate' language in the abstract is misleading: the fit fraction is a fit output, not a prediction. The molecular model fixes the line shape, not the rate. Second, there is no no-signal fit and no Δχ2, so the significance of the Tcs0 term is unquantified. Third, the model includes only the resonant contributions; no nonresonant background term is allowed, which could bias the whole fit. Fourth, the uncertainty on R only includes a4 and B(B−→K−D0K0); the compositeness coupling, the assumed 65% DK branching fraction, and the loop parameters α and μ are not propagated, and some are taken from the authors' own earlier papers. Fifth, Eq. (8) defines the reduced mass with D0 and K0 masses instead of D* and K* — likely a typo, but it changes the coupling if taken literally. Finally, the paper's claim that this channel can discriminate molecular vs compact tetraquark pictures is not backed by analysis: a compact tetraquark with the same J^P, mass, and width would give a very similar BW peak in D0K0, and no comparison is made.\n\nNone of these are fatal to the basic suggestion. The channel is interesting and the fit is a legitimate first look. But as it stands, the evidence for the Tcs contribution is inconclusive.\n\nWho gets value: hadron spectroscopy phenomenologists and the Belle II/LHCb groups looking for Tcs0(2900) in B decays. I would send it to a referee — the idea deserves the attention.","headline":"Good clean-channel proposal, but the 'predicted' fit fraction is a fit output and the paper never shows the Tcs signal is actually required.","tokens_in":9835,"tokens_out":4003,"would_cite":false,"duration_ms":42334,"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":"The paper predicts that Tcs0(2900)^0, treated as a D*0K*0 molecule, contributes a (9.72±3.92)% fit fraction to the D0K0 invariant mass spectrum of B−→K−D0K0, making that decay a clean discriminator between molecular and compact-tetraquark i","keywords":["Tcs0(2900)","tetraquark","D*K* molecule","exotic hadron","B meson decay","invariant mass spectrum","hadron spectroscopy","molecular state"],"falsifier":"A high-statistics measurement of the D0K0 invariant mass distribution in B−→K−D0K0: if no peak near 2892 MeV with a fit fraction around 10% emerges, or if the spectrum can be described equally well without Tcs0(2900)^0, the molecular interpretation fails. A model-independent check would extract the resonance parameters and compare the width and line shape to the molecular prediction.","tokens_in":8865,"feed_emoji":"⚛️","tokens_out":7319,"duration_ms":235552,"temperature":0.7,"pith_summary":"The paper proposes B−→K−D0K0 as the cleanest place to look for the exotic four-quark state Tcs0(2900)^0. If Tcs0(2900)^0 is a D*0K*0 molecule, the authors find it should leave a clear peak in the D0K0 mass spectrum, with a fit fraction of about (9.72±3.92)%, and that this channel is free of the conventional-meson backgrounds that clutter other B decays. A fit to the existing data reproduces the measured K−K0, D0K0, and D0K− distributions with χ²/d.o.f. ≈ 1.07. Because the D0K0 final state receives contributions only from isovector exotics, this process could settle whether Tcs0(2900)^0 is a molecular state or a compact tetraquark.","feed_headline":"B−→K−D0K0 should expose Tcs0(2900)0 at a ~10% fit fraction","feed_subtitle":"If the D*K* molecule picture holds, this clean decay channel can separate it from compact tetraquarks.","key_machinery":"The central object is Tcs0(2900)^0 as a D*0K*0 molecular state. The key machinery is the coupled production-decay amplitude: B− emits a D*0K*0 pair via external W emission, the pair rescatters through a two-meson loop into the molecular resonance, and the resonance propagates through a Breit-Wigner and decays to D0K0. The D*0K*0 coupling is fixed by the compositeness condition with λ̃=1, and the D0K0 coupling is fixed by the assumed 65% branching fraction; the loop integral is regularized dimensionally and includes K* width effects. The resulting amplitude, combined with rho/a0 background amplitudes and fitted to data, carries the argument.","core_discovery":"Treating Tcs0(2900)^0 as an S-wave D*0K*0 molecule, the paper shows that the decay B−→K−D0K0 proceeds through the production and rescattering of D*0K*0 into the molecular state, which then decays to D0K0. Including rho(770), rho(1450), and a0(980) contributions to the K−K0 system, the model fits the reported invariant mass distributions well and attributes a (9.72±3.92)% fit fraction to Tcs0(2900)^0 in the D0K0 spectrum. The authors argue this channel is clean because only possible isovector states like Tcs0(2900)^0 contribute; conventional charmed-strange mesons, the isoscalar X0,1(2900) states, and charmonium backgrounds are all absent.","pith_inferences":["A natural extension is to apply the same rescattering-plus-Breit-Wigner analysis to the charged partner Tcs0(2900)++ in a comparably clean final state, which would test isospin symmetry of the molecular picture.","Because the signal is a Breit-Wigner built from the molecular hypothesis, confirming the interpretation likely requires matching not just the peak position but also the predicted width and normalization; a compact-tetraquark model might produce a similar peak, so production rates in multiple channels would be needed.","The near-flat projection of the molecular state onto the K−K0 spectrum means future analyses can concentrate statistics on the D0K0 observable rather than the crowded K−K0 region.","A testable extension would compute the same fit fraction in a compact-tetraquark model; if the two predictions differ by more than the quoted uncertainty, this channel becomes a direct experimental arbiter between the two pictures."],"forward_implications":["If the molecular picture is correct, a high-statistics measurement of B−→K−D0K0 should reveal a D0K0 enhancement near 2892 MeV with a fit fraction around (9.72±3.92)%.","Because the D0K0 channel excludes conventional-meson backgrounds, observing that peak would be direct evidence for an absolutely exotic four-quark state.","The K−K0 near-threshold structure is explained by rho and a0 contributions, so the D0K0 peak is the only exotic signature needed in this decay.","Comparing the measured D0K0 line shape to the predicted molecular production amplitude would help distinguish D*K* molecules from compact tetraquarks or threshold effects.","The D0K− spectrum is reproduced through interference among the included resonances, implying no additional state is needed there."],"fun_headline_variants":["B−→K−D0K0 cleanly exposes Tcs0(2900)^0","Tcs0(2900)^0 signal in B−→K−D0K0 at ~10%","Probe tetraquark Tcs0(2900)^0 via clean B− decay","B−→K−D0K0: a clean test for exotic four-quark states","Molecular tetraquark Tcs0(2900)^0 visible in B−→K−D0K0"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The prediction rests on Tcs0(2900)^0 being a purely molecular D*0K*0 state (λ̃=1) with a 65% branching fraction to D0K0; if the state has a compact tetraquark core or a different DK coupling, the predicted signal and fit fraction change, and the fit cannot tell them apart because the signal is just a Breit-Wigner peak.","fun_headline_variants_meta":{"raw":{"variants":["B−→K−D0K0 cleanly exposes Tcs0(2900)^0","Tcs0(2900)^0 signal in B−→K−D0K0 at ~10%","Probe tetraquark Tcs0(2900)^0 via clean B− decay","B−→K−D0K0: a clean test for exotic four-quark states","Molecular tetraquark Tcs0(2900)^0 visible in B−→K−D0K0"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000545,"raw_usage":{"total_tokens":2461,"prompt_tokens":779,"completion_tokens":1682,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":523,"completion_tokens_details":{"reasoning_tokens":1553}},"tokens_in":523,"tokens_out":1682,"duration_ms":11690,"temperature":1.0,"reasoning_tokens":1553,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T12:48:47.910262+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A high-statistics measurement of the D0K0 invariant mass distribution in B−→K−D0K0: if no peak near 2892 MeV with a fit fraction around 10% emerges, or if the spectrum can be described equally well without Tcs0(2900)^0, the molecular interpretation fails. A model-independent check would extract the resonance parameters and compare the width and line shape to the molecular prediction.","supporting_citations":[],"review_version":1}