{"id":"35fb8fd9-469d-4069-9156-4326a763e96f","arxiv_id":"2507.18941","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The Ξ(1620) spectrum in Ξ_c → ππΞ decay shifts below the pole position, and the peak-to-cusp transition tracks the sign of the real part of the ¯KΛ scattering length.","lead":"Two theoretical models of the Ξ(1620) particle, one matching Belle data and one matching ALICE data, describe different physical states that cannot be smoothly connected. The paper computes the πΞ mass spectrum for each model and finds that the visible peak can sit below the true resonance pole because of threshold effects.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Spectrum shape claims in Eq. (5) depend on unstated production weights h_i; without a sensitivity study the 1599 MeV peak and the peak-to-cusp correlation are not established.","rationale":"The paper's central claim has two legs: (1) a correlation between the spectrum shape near the KbarLambda threshold and the sign of Re a0, and (2) a stronger threshold shift in the three-body decay (1599 MeV vs 1610 MeV pole). Both legs are computed from Eq. (5), which contains the unconstrained weights h_i. Unlike the model-interpolation path, which only affects the continuous demonstration of the correlation, the h_i are needed for every spectrum point: the x=0 model, the x=1 model, and the intermediate spectra. Without h_i, the absolute peak position and even the peak-vs-cusp classification are undefined; the reader cannot verify the figures or test the sensitivity. The paper also does not state that h_i are taken equal or derived from Ref. [20], so the omission is not merely a missing citation but an unspecified input. The interpolation path is a secondary concern: even if the path were physically motivated, the h_i problem would remain. I therefore agree with the reader's weakest assumption. A concrete sensitivity check over a plausible range of h_i would settle whether the qualitative conclusions survive. If they do, the paper is conditionally acceptable as a proceedings contribution; if not, the central claim should be weakened.","tokens_in":6470,"tokens_out":9916,"duration_ms":103051,"concrete_test":"Determine the h_i used in the figures (from Ref. [15] or by rerunning the code), then repeat the spectrum calculation of Fig. 2 with (i) all h_i = 1 and (ii) h_j = 1 with all other h_i = 0, and with a sign flip of h_j relative to the rescattering term. Also vary each h_i independently by a factor of 2 in magnitude. Check two observables: the peak position of the x=0 spectrum and the value of x at which the spectrum switches from a peak to a cusp. If the peak changes by more than ~5 MeV or the transition x shifts by more than 0.1 away from the crossing of Re a0, then the claimed correlation is not robust to the unspecified weights.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (5) defines the invariant mass distribution as |V_P (h_j + \\Sigma_i h_i G_i(M_inv) T_{ij}(M_inv))|^2 times phase space. The overall constant V_P cancels in the normalized shape, but the relative magnitudes and phases of the production weights h_i control the interference between the direct term h_j and the final-state rescattering. The headline quantitative results--the Model 1 peak at 1599 MeV, its shift below the pole at 1610 MeV (versus 1606 MeV in the two-body amplitude), and the point x~0.375 where the peak becomes a cusp--all come from this formula, yet the paper never states the h_i used to produce Fig. 2; it only says they represent channel weights. No sensitivity study is provided, and no argument from the weak decay Hamiltonian fixes the weights uniquely. If, for example, h_j is large and opposite in sign to the rescattering terms, the 1599 MeV peak can become a dip, and the transition point between peak and cusp can move away from the zero of Re a0. The central correlation claim is therefore not reproducible from the paper alone and could be an artifact of one unstated production model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the excited Ξ(1620) resonance within the chiral unitary approach. It uses two previously constructed models: Model 1, fitted to Belle mass/width data, and Model 2, fitted to the ALICE K−Λ scattering length. The authors interpolate between the two models by linearly varying the subtraction constants in Eq. (4), track the pole trajectory in Fig. 1, and compute the π+Ξ− invariant mass distribution for Ξc→ππΞ using the production-weighted final-state-interaction formula in Eq. (5). The main claims are that the spectral shape near the ¯KΛ threshold is strongly correlated with the sign of the real part of the ¯KΛ scattering length, that the Model 1 peak sits at 1599 MeV, well below the 1610 MeV pole energy, and that threshold effects are even more prominent in the three-body decay than in the two-body amplitude.","tokens_in":6668,"tokens_out":5122,"duration_ms":53786,"significance":"If the central claims hold, the paper delivers a useful and testable message: the Belle πΞ peak should not be read directly as the Ξ(1620) pole mass, because near-threshold coupled-channel dynamics shift the peak substantially in the three-body decay. The correlation between the spectral shape (peak vs. cusp) and the sign of Re a0 is a concrete, falsifiable diagnostic that can be applied to other near-threshold resonances. The paper also supports the view that the two models describe different eigenstates, although this conclusion is presented with limited evidence. The calculation uses the standard Weinberg-Tomozawa kernel and dimensional regularization, and the companion papers [11,15] provide the underlying framework; nevertheless, the present manuscript is not self-contained on the key inputs needed to reproduce the spectral results.","major_comments":[{"comment":"The production weights h_i that enter the invariant mass distribution in Eq. (5) are never specified, and no sensitivity study is provided. The main quantitative results of the paper—the Model 1 peak at 1599 MeV, its downward shift from the 1610 MeV pole, and the peak-to-cusp transition at x≈0.375—are all computed from this formula and therefore cannot be reproduced or assessed from the manuscript alone. Please provide the values (and if possible the derivation) of h_i, and demonstrate that the conclusions are stable under reasonable variations of these weights, e.g., by showing spectra for several choices of h_i or bounding the effect analytically.","section":"Sec. 2, Eq. (5)"},{"comment":"The conclusion in Sec. 3 that the Model 1 and Model 2 poles 'originate from different physical mechanisms' rests on the specific linear interpolation path in Eq. (4). Since the subtraction-constant space is multi-dimensional, an alternative path could in principle connect the two pole positions, so the claim of distinct eigenstates is path-dependent as presented. Please clarify whether this conclusion has been tested against different interpolation paths, or cite the systematic analysis in Ref. [15] that establishes it.","section":"Sec. 2, Eq. (4)"},{"comment":"The numerical values of the subtraction constants a_i, the meson decay constants, and the masses used in the models are not listed anywhere in the manuscript, so the calculation is not reproducible from this paper alone. Please include a table with these inputs or give precise pointers to the equations/tables in Ref. [11] where they are defined.","section":"Sec. 2, Eqs. (1)-(3)"}],"minor_comments":[{"comment":"The caption for the left panel describes the distribution as π+Ξ0, but the text and abstract consistently discuss the π+Ξ− channel; please correct the caption.","section":"Fig. 2 caption"},{"comment":"The statement that the spectral shape changes from a peak to a cusp 'around the same value' of x is based on interpolation points spaced by 0.2; please state the precise x value where the transition occurs and how it is defined, or soften the claim accordingly.","section":"Sec. 3, Fig. 2"},{"comment":"The correlation between the spectral shape and the sign of Re a0 is presented without a quantitative measure; a simple quantification (e.g., the height of the maximum relative to the threshold value as a function of Re a0) would strengthen the claim.","section":"Sec. 3, Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, so some reliance on companion papers is expected. However, the complete omission of h_i is a genuine reproducibility gap for the paper's headline spectral-shape claims, and the missing a_i values make the interpolation and scattering-length results unverifiable from the text. The path-dependence of the pole connection claim is a second concern, but it is less central to the threshold-effect message. With a short addition of the numerical inputs and a sensitivity check, the paper would be acceptable for these proceedings."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful proceedings paper, not a breakthrough, and the main new numbers are plausible but not fully standalone. The genuinely new bit is the calculation of the π+Ξ− invariant mass spectrum in Ξ_c → ππΞ for the two chiral unitary models from Ref [11], plus the interpolation path between them. The headline result, that the Model 1 peak sits at 1599 MeV while the pole sits at 1610 MeV, and that the three-body shift is larger than the two-body shift (1606 MeV), is a concrete, checkable claim and worth having on record. The peak-to-cusp transition tracking the zero of Re a0 is also clearly presented.\n\nThe calculation is standard: Weinberg-Tomozawa kernel, dimensional-regularized loop, coupled-channel equation. I don't see an internal inconsistency, and the pole trajectory showing that the two fitted models land on different Riemann sheets is a fair reading of the earlier work. The paper is not circular; fitting to Belle and ALICE inputs is ordinary model construction.\n\nWhere it gets soft is Eq. (5). The production weights h_i are never given, V_P is just a constant, and there is no sensitivity scan. The stress-test note is correct: with arbitrary relative phases and magnitudes of h_i, the position of the peak, and even the peak-to-cusp transition, can move. So the specific numbers 1599 MeV and x≈0.375 are not reproducible from the paper alone. The paper also does not overlay the Belle data, which would have been the natural way to see whether the threshold-shift explanation actually works. The subtraction constants are omitted; they are presumably in Ref [11], but a proceedings paper can still list them or point to a table.\n\nNone of this makes the central idea wrong. The correlation between the sign of Re a0 and peak-vs-cusp near threshold is known from two-body studies [21,22], and the present work extends it to a three-body decay. For a reader interpreting the Belle πΞ peak as the Ξ(1620) mass, the caution about threshold effects is well taken. But the paper overstates what it establishes: without the production model, it shows that some choices of h_i produce a large shift, not that the three-body threshold effect is necessarily more prominent than the two-body one.\n\nWho is this for? Practitioners in hadron spectroscopy, especially those working on coupled-channel fits to Belle and ALICE data. Deserves a serious referee: yes, it is topical, short, and has a concrete prediction, but the referee should ask for the h_i values and a sensitivity study before publication. I would not cite the 1599 MeV number until that is supplied.","headline":"Useful proceedings paper with a concrete threshold-shift prediction for Ξ_c decay, but the numerical peak position is not reproducible until the production weights are specified and tested.","tokens_in":7248,"tokens_out":2719,"would_cite":false,"duration_ms":29917,"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 argues that the $\\pi^+\\Xi^-$ peak in $\\Xi_c \\to \\pi\\pi\\Xi$ sits at $1599$ MeV while the $\\Xi(1620)$ pole sits at $1610$ MeV, and that the line shape near the $\\bar{K}\\Lambda$ threshold tracks the sign of the real part of the…","keywords":["Xi(1620)","chiral unitary approach","coupled-channel scattering","threshold effects","scattering length","invariant mass spectrum","Xi_c decay","pole trajectory"],"falsifier":"A high-statistics measurement of the $\\pi^+\\Xi^-$ invariant mass distribution in $\\Xi_c \\to \\pi\\pi\\Xi$ that resolves the line shape near the $\\bar{K}\\Lambda$ threshold would test the claim: a cusp maximum at the threshold would support a negative real scattering length, while a peak near 1599 MeV below the 1610 MeV pole would confirm the threshold-shift mechanism of Model 1.","tokens_in":6189,"feed_emoji":"⚛️","tokens_out":8535,"duration_ms":81934,"temperature":0.7,"pith_summary":"The paper argues that the $\\pi^+\\Xi^-$ peak seen in $\\Xi_c \\to \\pi\\pi\\Xi$ decay is not a direct reading of the $\\Xi(1620)$ pole mass: in the model based on the experimental resonance parameters, the three-body peak sits at $1599$ MeV while the pole sits at $1610$ MeV. As one continuously interpolates between that model and a model based on the measured $K^-\\Lambda$ scattering length, the line shape near the $\\bar{K}\\Lambda$ threshold changes from a peak to a cusp exactly when the real part of the $\\bar{K}\\Lambda$ scattering length changes sign. The two models' poles never meet on the Riemann sheets, so the two poles correspond to different eigenstates even though both have been associated with the $\\Xi(1620)$. The upshot is that experimental $\\pi\\Xi$ spectra must be analyzed with coupled-channel threshold effects built in, not by assigning the observed peak energy directly to a resonance mass.","feed_headline":"Threshold shifts the Xi(1620) peak 11 MeV below its pole","feed_subtitle":"A chiral coupled-channel analysis links the peak-to-cusp change in the pi+ Xi- spectrum to the Kbar-Lambda scattering length sign.","key_machinery":"The load-bearing object is the coupled-channel scattering amplitude $T_{ij}(W)$ defined by $T = V + VGT$ with the Weinberg-Tomozawa kernel $V_{ij}^{\\rm WT}$ and dimensionally regularized loop functions $G_k(W;a_k)$, together with the model interpolation $a_i(x)=x a''_i + (1-x)a'_i$ that continuously connects the two parameter sets. The decay spectrum is generated from this amplitude through Eq. (5), where the weak-production vertex $V_P$ is a constant and the channel weights $h_i$ weight each intermediate meson-baryon channel. The correlation between line shape and the real part of the $\\bar{K}\\Lambda$ scattering length $a_0$ is the mechanism that turns a peak into a cusp when $x$ crosses $\\sim0.375$.","core_discovery":"Within the chiral unitary approach, the authors construct two models of the $\\Xi(1620)$: Model 1 reproduces the experimentally reported mass and width and has a pole at $z_1 = 1610 - 30i$ MeV on the $[bbtttt]$ Riemann sheet, while Model 2 reproduces the measured $K^-\\Lambda$ scattering length and has a pole at $z_2 = 1726 + 80i$ MeV on the $[ttbttt]$ sheet. By linearly interpolating the subtraction constants between the models, they find that $z_1$ never moves onto the sheet containing $z_2$, and conclude that the two poles originate from different physical mechanisms rather than from one state seen in two parametrizations. Computing the $\\pi^+\\Xi^-$ invariant mass distribution in $\\Xi_c \\to \\pi\\pi\\Xi$ with Eq. (5), they find that the spectral shape near the $\\bar{K}\\Lambda$ threshold is governed by the sign of the real part of the $\\bar{K}\\Lambda$ scattering length: positive $\\mathrm{Re}\\,a_0$ gives a peak, negative gives a cusp, with the transition near the interpolation point $x\\sim0.375$. The Model 1 spectrum peaks at $1599$ MeV, below the $1610$ MeV pole, and this threshold shift is larger in the three-body decay than in the two-body scattering amplitude, where the peak sits at $1606$ MeV.","pith_inferences":["The authors do not test the stability of their spectrum against the production weights $h_i$; varying those weights over a plausible range is a natural next step, since the 1599 MeV peak position and the peak-to-cusp transition could shift if the production inputs change.","A high-statistics measurement that resolves a cusp rather than a peak at the $\\bar{K}\\Lambda$ threshold would favor a negative real scattering length, while a peak near 1599 MeV below the 1610 MeV pole would confirm the threshold-shift mechanism of Model 1.","The same interpolation-and-spectrum strategy could be applied to other three-body decays where a resonance sits near a two-body threshold, making the scattering-length sign a common ordering principle for line shapes.","Because the threshold effect is larger in the three-body process than in the two-body amplitude, analyses of other heavy-hadron three-body decays with nearby thresholds may need even larger corrections than two-body estimates suggest."],"forward_implications":["A measured $\\pi^+\\Xi^-$ peak energy cannot be identified with the $\\Xi(1620)$ pole position; in Model 1 the three-body peak is 11 MeV below the pole, so an analysis of the experimental spectrum must include the decay dynamics.","The sign of the real part of the $\\bar{K}\\Lambda$ scattering length predicts the line shape: positive values produce a peak near threshold, negative values a cusp, so the observed spectral shape can act as a diagnostic for the scattering length.","The absence of a pole connection during interpolation indicates that the two descriptions of the $\\Xi(1620)$ correspond to different eigenstates, which must be treated as distinct in phenomenological comparisons.","Threshold effects are stronger in the three-body invariant mass distribution than in the two-body amplitude, so three-body decay data are a sharper probe of threshold physics.","Even when the pole lies above the $\\bar{K}\\Lambda$ threshold, the spectrum can still show a peak below threshold, so pole position and peak position need not even lie on the same side of the threshold."],"supporting_citations":[{"why":"provides the experimental $\\pi^+\\Xi^-$ mass spectrum and the $\\Xi(1620)$ mass and width that define Model 1.","marker":"[4]"},{"why":"provides the experimentally determined $K^-\\Lambda$ scattering length used to define Model 2.","marker":"[5]"},{"why":"is the previous work that constructs the two chiral unitary models whose poles are compared and interpolated here.","marker":"[11]"},{"why":"is the companion study giving the two-body peak at 1606 MeV and the detailed pole-trajectory analysis.","marker":"[15]"},{"why":"supplies the $\\Xi_c \\to \\pi\\pi\\Xi$ decay amplitude formula used to compute the invariant mass spectrum.","marker":"[20]"},{"why":"established the connection between spectral shape near a threshold and the sign of the real part of the scattering length.","marker":"[21]"},{"why":"reinforces the scattering-length-sign correlation for the $\\bar{K}\\Lambda$ channel.","marker":"[22]"}],"fun_headline_variants":["Xi(1620) peak shifts below pole: threshold effect","Three-body decay widens Xi(1620) peak shift to 11 MeV","Sign of Kbar-Lambda scattering length flips peak to cusp","Two Xi(1620) poles traced to different mechanisms","Peak-to-cusp change driven by scattering length sign"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The spectrum calculation assumes the weak-decay production amplitude is constant and leaves the relative weights of the intermediate channels unspecified, so the predicted peak position at 1599 MeV and the peak-to-cusp transition could move if those inputs are changed.","fun_headline_variants_meta":{"raw":{"variants":["Xi(1620) peak shifts below pole: threshold effect","Three-body decay widens Xi(1620) peak shift to 11 MeV","Sign of Kbar-Lambda scattering length flips peak to cusp","Two Xi(1620) poles traced to different mechanisms","Peak-to-cusp change driven by scattering length sign"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000628,"raw_usage":{"total_tokens":2911,"prompt_tokens":962,"completion_tokens":1949,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":1873}},"tokens_in":578,"tokens_out":1949,"duration_ms":13350,"temperature":1.0,"reasoning_tokens":1873,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:06:00.326598+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A high-statistics measurement of the $\\pi^+\\Xi^-$ invariant mass distribution in $\\Xi_c \\to \\pi\\pi\\Xi$ that resolves the line shape near the $\\bar{K}\\Lambda$ threshold would test the claim: a cusp maximum at the threshold would support a negative real scattering length, while a peak near 1599 MeV below the 1610 MeV pole would confirm the threshold-shift mechanism of Model 1.","supporting_citations":[{"cited_title":"Sumihamaet al., Phys","cited_arxiv_id":null,"evidence_quote":"provides the experimental $\\pi^+\\Xi^-$ mass spectrum and the $\\Xi(1620)$ mass and width that define Model 1."},{"cited_title":"Acharyaet al., Phys","cited_arxiv_id":null,"evidence_quote":"provides the experimentally determined $K^-\\Lambda$ scattering length used to define Model 2."},{"cited_title":"Nishibuchi and T","cited_arxiv_id":null,"evidence_quote":"is the previous work that constructs the two chiral unitary models whose poles are compared and interpolated here."},{"cited_title":"Miyahara, T","cited_arxiv_id":null,"evidence_quote":"supplies the $\\Xi_c \\to \\pi\\pi\\Xi$ decay amplitude formula used to compute the invariant mass spectrum."}],"review_version":2}