{"id":"c366cb0a-636b-442f-a1d2-e86b336a75be","arxiv_id":"2501.11408","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"By using realistic dispersive pion-kaon interactions and relativistic corrections, the authors fit ALICE femtoscopy data and obtain source radii of about 0.35 to 0.67 fm, well below the typical 1 fm.","lead":"This paper re-analyzes ALICE measurements of pion-kaon momentum correlations and shows that realistic pion-kaon interactions plus relativistic corrections describe the data well. It extracts much smaller source sizes than usual, and argues the standard formula used for this extraction may be too simple for light mesons.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The small source radii depend on fits that extend above the Kη threshold, where the paper's own formalism is declared invalid; a truncated fit may not reproduce them.","rationale":"The reader identifies on-shell factorization as the weakest assumption, which is reasonable for interpreting R as a physical source size. I agree that the physical meaning of R is the core issue, but the more immediate, testable vulnerability is the fit domain: the formalism is openly invalid above the Kη threshold, and the plotted data extend well beyond it. Since the headline result is the size of R, a test that excludes the invalid region directly probes the claim. The paper is a proceedings with no error bars or code, and the authors call the results preliminary, so a conditional verdict is appropriate; the correct response is to request the restricted fit as a condition of acceptance, not to reject. This does not change the reader's conditional verdict, hence UNCHANGED.","tokens_in":5099,"tokens_out":4231,"duration_ms":46946,"concrete_test":"Refit each ALICE dataset using exactly the same relativistic + coupled-channels machinery, but with the k* range truncated at the Kη threshold. Compute the threshold momentum from the physical masses (mπ = 0.1396 GeV, mK = 0.4937 GeV, mη = 0.5478 GeV), which gives k*_thr ≈ 0.38 GeV. Report R, λ, κ, their uncertainties, and χ² per point for both the truncated and full fits. If the truncated-fit R values move substantially toward the ~1 fm literature value, or if the reported small radii only emerge when data above the threshold are included, the small-radius conclusion is a boundary artifact. This check also clarifies whether the claimed 'good description' depends on the invalid region.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central physical message is that the fitted source radii (R = 0.35, 0.38, 0.67 fm) are anomalously small compared with the ~1 fm literature value. The most load-bearing unverified step is not the philosophical validity of on-shell factorization, but the fact that the fits are displayed against data up to k* = 0.7 GeV, while the paper's own formalism is defined only below the Kη threshold (k* ≈ 0.38 GeV for πK pairs). Section 4 states this explicitly: 'the dashed black line marks the opening of the Kη threshold, where our formalism is formally no longer valid, although it still yields a fairly good qualitative description.' If data above that threshold participate in the χ² minimization, the extracted R and λ can be biased by a regime where neither the dispersive CFD amplitude nor the coupled-channel extension is justified. The paper does not state the fit range, the χ² per datapoint, or the definition of the red bands; without these, 'well described' is not quantified and the small-R conclusion is not robust. This is a self-identified boundary issue, not an external objection: the authors themselves present the result as preliminary.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings contribution argues that the ALICE π+K_S femtoscopic s-wave correlation data, previously analyzed with a relativistic Breit-Wigner (BW) parametrization of the πK interaction, can instead be described using a realistic, dispersively constrained πK amplitude (the CFD parametrization of Peláez and Rodas), together with relativistic corrections and coupled-channel effects. The authors show that with only three fit parameters per dataset (source radius R, correlation strength λ, and a normalization κ slightly different from unity) they reproduce the three ALICE datasets, and they obtain source radii R = 0.35, 0.38, and 0.67 fm. They interpret these values as being smaller than the typical ~1 fm radii obtained in the literature, and they suggest that this discrepancy may indicate a failure of the on-shell factorization approximation underlying the standard Lednicky-Lyuboshits (LL) formula.","tokens_in":5416,"tokens_out":2370,"duration_ms":27876,"significance":"If the results hold up, the paper makes a valuable methodological point: realistic πK interactions derived from scattering data, rather than a BW parametrization, should be used in femtoscopic analyses, and the non-trivial energy dependence of the κ/K*0(700) region matters for extracting source parameters. The paper also raises a potentially important physics question about the validity of on-shell factorization for relativistic light mesons. The authors are appropriately careful to present the results as preliminary, and they explicitly flag the Kη threshold as a limit of their formalism. The main novelty is the combination of the dispersive CFD amplitude with relativistic corrections and coupled channels in a femtoscopic context, and the observation that this changes the extracted source radii. However, the paper is a short proceedings contribution and does not yet provide the quantitative support needed to make the small-radius claim robust.","major_comments":[{"comment":"The central claim that the fitted source radii are anomalously small relies on fits that are displayed up to k* = 0.7 GeV, while the paper states that the formalism is formally valid only below the Kη threshold (k* ≈ 0.38 GeV). The manuscript does not state the actual fit range used in the χ² minimization. If data above the Kη threshold contribute to the fit, the extracted R and λ could be biased by a region where neither the CFD amplitude nor the coupled-channel extension is justified. The authors should report fits restricted to k* below the Kη threshold and show that the small radii persist, or otherwise quantify the sensitivity of R and λ to the fit range.","section":"Sec. 4, Fig. 3"},{"comment":"No uncertainties are quoted for R, λ, or κ, and the red bands in Fig. 3 are not defined. Without confidence intervals or a goodness-of-fit measure (χ² per degree of freedom, or a comparison of fit quality with the ALICE BW fits), the statement that the data are 'well described' is not quantitatively supported, and the significance of the difference from the ~1 fm literature radii cannot be assessed.","section":"Sec. 4, Fig. 3"},{"comment":"The paper interprets the small values of R as evidence that the on-shell factorization approximation underlying the LL formula may be invalid for relativistic light mesons. This is a plausible interpretation, but it is not established by the present analysis, because the same approximation is used to obtain the fits. A stronger test would be to compare the extracted radii with an independent determination, for example from ππ or KΛ femtoscopy with the same event classes, or to perform a calculation that avoids the on-shell factorization and check whether the fitted R values change. Without such a cross-check, the small-R conclusion remains model-dependent rather than a demonstrated physical effect.","section":"Sec. 4"},{"comment":"The paper correctly criticizes the ALICE BW parametrization for neglecting the I = 3/2 component and inelastic effects, but the quantitative impact of these effects on the final fitted radii is not shown. Fig. 2 compares correlation functions at fixed R and λ, yet the fitted R and λ values in Fig. 3 are the result of the full model. It would be helpful to report how R and λ change when each improvement (relativistic corrections, CFD amplitude, coupled channels) is added separately, to identify which ingredient drives the small radii.","section":"Sec. 2, Eq. (1)"}],"minor_comments":[{"comment":"The relativistic corrections are described only by reference to previous work; since the central results depend on them, the authors should at least give the explicit form of the modified F1 and F2 functions or the Bethe-Salpeter equation used, or state more clearly that this is a proceedings summary of a longer paper.","section":"Sec. 3"},{"comment":"The symbol k* is used both for the pair center-of-mass momentum and, in Eq. (2), for the momentum in the scattering amplitude; this is standard in femtoscopy but could be clarified to avoid confusion with the Mandelstam variable s.","section":"Sec. 1"},{"comment":"The red bands in Fig. 3 are not described in the text. The authors should state whether they represent statistical uncertainties, systematic uncertainties, or the spread from the CFD parametrization.","section":"Sec. 4"},{"comment":"The phrase 'surprisingly smaller' is used in both the abstract and Sec. 4. Since the paper itself questions the validity of the factorization model, the word 'surprisingly' may be overstated; a more neutral phrasing would better reflect the preliminary nature of the result.","section":"Abstract and Sec. 4"},{"comment":"Reference [12] is a preprint (arXiv:2410.08880) that is cited for the relativistic formalism; the authors should check whether a published version exists and update the citation if so.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is a conference proceedings contribution, and the bar for a proceedings paper is lower than for a full article. However, the specific numerical claim about small source radii is potentially influential and is currently not supported by a stated fit range, uncertainties, or goodness-of-fit. The authors appear to be aware of the limitations and present the results as preliminary, which is commendable. If the fit-range and uncertainty issues are addressed in a revised version, the paper could be acceptable as a proceedings contribution; otherwise the central quantitative claim remains unsubstantiated."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take: this is a preliminary proceedings that makes a real methodological point and has one load-bearing gap you should be aware of. The new thing is the combined application of the dispersive CFD piK amplitudes from Pelaez-Rodas, Bethe-Salpeter relativistic corrections, and coupled channels to the ALICE pi+KS femtoscopy data. That combination cuts the per-dataset fit parameters from 6 to 3 and gives source radii of 0.35, 0.38, 0.67 fm, well below the ~1 fm typical in the literature. The authors deserve credit for a few things: the FSI amplitude is fixed from scattering data rather than fit to the correlation function themselves, so the good description is not enforced by construction. The plots in Fig. 3 look genuinely reasonable. And they are transparent about the limitations, including the K-eta threshold boundary in the caption itself.\n\nThe soft spot, and I think the real one, is that the central scientific message is the small source radius, but the fits as displayed extend to k* ~ 0.7 GeV, while the formalism is only valid below the K-eta threshold at about 0.38 GeV. The paper never states the fit range used in the minimization, nor gives chi2 per point, nor defines the red bands. If the data above threshold enter the chi2, R and lambda can be biased by a region where the CFD amplitude and coupled-channel extension are not justified. That ground is shaky even by the authors' own admission: the caption says 'formally no longer valid' and only 'qualitatively good' there. Without a truncated fit below threshold, I can't distinguish a small physical source from a modeling artifact. Secondary issues: no uncertainties on R and lambda, and the relativistic/coupled-channel derivations are only referenced, which is acceptable for a proceedings but limits how self-contained the check is.\n\nOverall, the reader's conditional verdict is right. The idea is important—if LL on-shell factorization really does fail for relativistic light mesons, that reverberates on ALICE's kappa conclusions—but this paper doesn't yet prove it. What it does is clear groundwork and an argument for why a careful look matters. I'd like to see the same group come back with a fit restricted to the valid regime, explicit error bars, and a statement of fit ranges and chi2. Then the small-R claim would be testable.\n\nFor peer review: yes, send it out if submitted as a regular paper. The question matters, and the method is a credible advance over the Breit-Wigner treatment. In the current proceedings form it's a conference talk, not a final answer. I'd bring it to a reading group as a useful prompt to think about factorization approximations.","headline":"Preliminary but promising: realistic dispersive piK amplitudes plus relativistic corrections describe ALICE pi+KS data with 3 parameters and small source radii, but the headline radius is not yet robust because the fits extend beyond the formalism's K-eta validity boundary.","tokens_in":5970,"tokens_out":2637,"would_cite":false,"duration_ms":28277,"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":"This paper argues that ALICE's $\\pi^+ K_S$ femtoscopic correlations can be described with realistic pion-kaon interactions and relativistic corrections, yielding source radii of 0.35, 0.38, and 0.67 fm rather than the usual ~1 fm.","keywords":["femtoscopic correlations","pion-kaon scattering","kappa/K*0(700)","Lednicky-Lyuboshits formula","relativistic corrections","dispersive analysis","source radius","ALICE pp collisions"],"falsifier":"Refit the three ALICE datasets with the full two-body Bethe-Salpeter wave function, dropping the on-shell factorization of the amplitude; if the best-fit source radii return to about 1 fm with a comparable $\\chi^2$, the small radii are an artifact of the factorization rather than a property of the source.","tokens_in":4943,"feed_emoji":"⚛️","tokens_out":13807,"duration_ms":125474,"temperature":0.7,"pith_summary":"The paper tries to establish that the $\\pi^+ K_S$ femtoscopic correlations measured by ALICE in $pp$ collisions can be described with realistic pion-kaon interactions and relativistic corrections, rather than with the non-relativistic Breit-Wigner model used by ALICE. Combining a dispersive parametrization of $\\pi K$ scattering (the Constrained Fits to Data, or CFD, amplitude with both isospin components and inelastic channels) with a relativistic version of the Koonin-Pratt formula, the authors fit the three ALICE datasets with only one normalization, the source radius $R$, and the correlation strength $\\lambda$. Their fitted radii, $R = 0.35$, $0.38$, and $0.67$ fm, are smaller than the roughly $1$ fm values typical in the literature. If the result holds, the standard on-shell factorization behind the Lednicky-Lyuboshits formula would need to be revisited for relativistic light mesons, and so would conclusions about the $\\kappa/K^*_0(700)$ resonance drawn from the simpler model.","feed_headline":"Realistic πK interactions shrink femtoscopy radii","feed_subtitle":"A dispersive πK amplitude plus relativity fits ALICE data with 3 parameters and returns source radii of 0.35–0.67 fm","key_machinery":"The carrying object is the two-particle correlation function $C(k^*) = \\int S(r)\\,|\\psi(k^*,r)|^2 d^3r$ in the Koonin-Pratt formalism. The standard Lednicky-Lyuboshits approximation assumes a Gaussian source, non-relativistic kinematics, and on-shell factorization of the scattering amplitude $f(k^*)$; the paper replaces the non-relativistic propagators and integration measure with relativistic ones derived from the Bethe-Salpeter equation, and replaces the ALICE Breit-Wigner parametrization of the $\\kappa/K^*_0(700)$ with the dispersive CFD parametrization of $\\pi K$ scattering data. That combination of a realistic amplitude, coupled channels, and relativistic kinematics is what reduces the fit parameters and produces the small radii.","core_discovery":"The central claim is that the interaction and the kinematics, not the source, are the main missing ingredients in previous fits. Once the $\\pi K$ s-wave amplitude is taken from a dispersive analysis that reproduces the $\\kappa/K^*_0(700)$ pole and includes the $I = 3/2$ component and coupled-channel effects, and once the wave function is computed with relativistic propagators and measure from the Bethe-Salpeter equation, the same interaction describes all three ALICE datasets. The fits need three parameters per dataset, versus six in the ALICE analysis, and yield source radii $R = 0.35$, $0.38$, $0.67$ fm. The authors state that these small values may raise questions about the validity of the widely used on-shell factorization models for relativistic light mesons, as well as the conclusions about the nature of the $\\kappa/K^*_0(700)$ drawn in the ALICE paper.","pith_inferences":["Cross-checking the same events with identical-pion HBT radii would distinguish a genuinely compact $\\pi K$ source from an artifact of the on-shell factorization: if the HBT radii stay near 1 fm while the $\\pi K$ fits demand 0.35–0.67 fm, the factorization is the likely problem.","Applying the same relativistic dispersive treatment to other kaon-containing pairs, such as $\\pi^+ K^-$ or $K^+ K^-$, would show whether the small radii are channel-specific or a general feature of kaon femtoscopy.","Because the paper's formalism is strictly valid only below the $K\\eta$ threshold, a coupled-channel extension above it is a natural next step; it would test whether the small radii survive once the high-$k^*$ region is treated exactly."],"forward_implications":["The same fixed $\\pi K$ interaction can be used across different multiplicity and transverse-momentum classes, so future femtoscopic fits do not need to refit resonance parameters for each dataset.","Because the realistic amplitude suppresses the interaction near threshold compared with the Breit-Wigner, the claim that the $\\kappa/K^*_0(700)$ is a non-ordinary, broad state is compatible with the femtoscopic data only when the dispersive amplitude is used.","Relativistic corrections change $C(k^*)$ by roughly 20% near threshold, so light meson pairs like $\\pi K$ need relativistic treatment before source radii can be trusted.","If the fitted radii are physical, the $\\pi^+ K_S$ emitting source in these $pp$ collisions is considerably more compact than the typical ~1 fm hadronic source."],"supporting_citations":[{"why":"Supplies the three ALICE $\\pi^+ K_S$ correlation datasets and the Breit-Wigner analysis that the paper improves.","marker":"[4]"},{"why":"Supplies the dispersive CFD parametrization of $\\pi K$ scattering used as the realistic interaction, including the $\\kappa/K^*_0(700)$ pole and the $I=3/2$ component.","marker":"[13]"},{"why":"Defines the Lednicky-Lyuboshits formula whose on-shell factorization and non-relativistic kinematics the paper corrects.","marker":"[7]"},{"why":"Provides the Bethe-Salpeter equation used to construct relativistically improved pair wave functions.","marker":"[10]"},{"why":"Gives the relativistic replacement for the non-relativistic propagators and integral measure in the correlation formula.","marker":"[11]"},{"why":"Also supplies the relativistic treatment of propagators and coupled channels for the pair wave-function.","marker":"[12]"},{"why":"One of the two $\\pi K$ scattering data sets that constrain the dispersive amplitude.","marker":"[8]"},{"why":"The other $\\pi K$ scattering data set used to fix the realistic interaction.","marker":"[9]"}],"fun_headline_variants":["New πK interactions from dispersive analysis shrink ALICE femtoscopy radii","Three parameters fit ALICE πK femtoscopy with dispersive interactions","Relativistic πK waves yield source radii below 0.7 fm in ALICE data","Model-independent πK amplitude challenges femtoscopy factorization","ALICE femtoscopy radii shrink with realistic πK interactions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the pair wave function can still be written as a free wave times an interaction amplitude evaluated at the measured momentum, even after the relativistic corrections are applied; if that on-shell factorization fails, the small source radii are a modeling artifact rather than the true source size.","fun_headline_variants_meta":{"raw":{"variants":["New πK interactions from dispersive analysis shrink ALICE femtoscopy radii","Three parameters fit ALICE πK femtoscopy with dispersive interactions","Relativistic πK waves yield source radii below 0.7 fm in ALICE data","Model-independent πK amplitude challenges femtoscopy factorization","ALICE femtoscopy radii shrink with realistic πK interactions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000925,"raw_usage":{"total_tokens":3936,"prompt_tokens":885,"completion_tokens":3051,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":501,"completion_tokens_details":{"reasoning_tokens":2959}},"tokens_in":501,"tokens_out":3051,"duration_ms":21523,"temperature":1.0,"reasoning_tokens":2959,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:17:11.568600+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refit the three ALICE datasets with the full two-body Bethe-Salpeter wave function, dropping the on-shell factorization of the amplitude; if the best-fit source radii return to about 1 fm with a comparable $\\chi^2$, the small radii are an artifact of the factorization rather than a property of the source.","supporting_citations":[{"cited_title":"Astonet al., Nucl","cited_arxiv_id":null,"evidence_quote":"One of the two $\\pi K$ scattering data sets that constrain the dispersive amplitude."},{"cited_title":"Estabrooks, R","cited_arxiv_id":null,"evidence_quote":"The other $\\pi K$ scattering data set used to fix the realistic interaction."}],"review_version":1}