Description of femtoscopic correlations with realistic pion-kaon interactions: the $\kappa/K^*_0(700)$ case

A. Canoa; E. Ruiz Arriola; J. Nieves; J. R. Pel\'aez; J. Ruiz de Elvira; M. Albaladejo

REVIEW 4 major objections 5 minor 13 references

Description of femtoscopic correlations with realistic pion-kaon interactions: the $\kappa/K^*_0(700)$ case

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2501.11408 v1 pith:XXGB7NH6 submitted 2025-01-20 hep-ph hep-exnucl-th

A. Canoa , M. Albaladejo , J. Nieves , J. R. Peláez , E. Ruiz Arriola , J. Ruiz de Elvira This is my paper · ORCID

classification hep-phhep-exnucl-th

keywords femtoscopiccorrelationspion-kaonscatteringkappa/K*0(700)Lednicky-LyuboshitsformularelativisticcorrectionsdispersiveanalysissourceradiusALICEppcollisions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

Overall, 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.

For 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.

Referee Report

4 major / 5 minor

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.

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 (4)

[Sec. 4, Fig. 3] 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.
[Sec. 4, Fig. 3] 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.
[Sec. 4] 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.
[Sec. 2, Eq. (1)] 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.

minor comments (5)

[Sec. 3] 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.
[Sec. 1] 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.
[Sec. 4] 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.
[Abstract and Sec. 4] 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.
[References] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the piK interaction is fixed from independent scattering data, and the ALICE correlations are fit only through kappa, R, and lambda.

full rationale

The paper's central input, the realistic piK interaction, is not fitted to the femtoscopic data. It is the CFD dispersive parametrization of piK scattering data from ref. [13], and Fig. 1 shows it against the external scattering data of Aston et al. and Estabrooks et al. The ALICE correlation data are an independent external benchmark. The only parameters fitted to those data are an overall normalization kappa, the source radius R, and the correlation strength lambda. The relativistic corrections are imported from refs. [11,12] via the Bethe-Salpeter equation, but that is a published formalism, not a parameter adjusted to the target data; the author overlap in those citations does not make the input equal to the output. The explicit limitation that the formalism is formally invalid above the K-eta threshold is an acknowledged validity boundary, not a circular step. No equation in the paper reduces to its own input by construction, and no fitted parameter is renamed as a prediction. The paper is self-contained against external scattering and femtoscopic data, so the circularity score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a standard femtoscopy framework, a model assumption about the source and the on-shell factorization, and an interaction input from a previous dispersive analysis. The only free parameters are the per-dataset radius, strength, and normalization. No new particles or entities are introduced. The most fragile item is the explicit use of the model above the K_eta threshold where validity is stated to end.

free parameters (5)

Source radius R (dataset 1: 100% multiplicity, kT>0) = 0.35 fm
Fit parameter in the correlation model, quoted in Fig. 3 Fit 1.
Source radius R (dataset 2: 100% multiplicity, kT<0.5 GeV) = 0.38 fm
Fit parameter in the correlation model, quoted in Fig. 3 Fit 2.
Source radius R (dataset 3: 5% multiplicity, kT<0.5 GeV) = 0.67 fm
Fit parameter in the correlation model, quoted in Fig. 3 Fit 3.
Correlation strength lambda (datasets 1,2,3) = 0.23, 0.30, 0.89
Fit parameters accounting for pair purity; values from Fig. 3.
Overall normalization kappa (per dataset) = within 1% of 1 (values not given)
Additional fit parameter per dataset, stated in Sec. 4 to differ from 1 by less than 1%.

assumptions (5)

domain assumption Koonin-Pratt formula with a normalized Gaussian source S(r)
Adopted as the definition of the correlation function; the Gaussian source is standard in femtoscopy (Sec. 1).
domain assumption On-shell factorization of the scattering amplitude in the Lednicky-Lyuboshits formula
Assumed in Eq. (1) and in the relativistic extension; the paper itself questions its validity for light mesons (Secs. 2 and 4).
domain assumption The piK interaction is isospin 1/2 plus 3/2 with coupled channels as given by the dispersive CFD parametrization
The amplitude is taken from ref. [13], not re-derived here; the coupling to pi+KL and pi0K+ is included (Sec. 3).
standard math The relativistic wave function is obtained from the Bethe-Salpeter equation in the approximation of refs. [11,12]
The relativistic formalism is cited from prior work; the paper relies on its validity without reproducing the derivation (Sec. 3).
ad hoc to paper Fits are valid beyond the K_eta threshold
The authors state the formalism is formally no longer valid above the K_eta threshold, yet still extend the fit to higher k* and quote resulting radii (Sec. 4, Fig. 3 caption).

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Cite this review

Pith. "Pith review of Description of femtoscopic correlations with realistic pion-kaon interactions: the $\kappa/K^*_0(700)$ case." pith.science (2026). https://pith.science/paper/XXGB7NH6

@misc{pith2026250111408,
  author       = {Pith},
  title        = {Pith review of: Description of femtoscopic correlations with realistic pion-kaon interactions: the $\kappa/K^*_0(700)$ case},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XXGB7NH6}},
  note         = {Machine review of arXiv:2501.11408}
}

abstract

In this work, we show how $\pi^+ K_S$ femtoscopic correlations, recently reported by ALICE collaboration in $ pp $ collisions, can be well described taking into account relativistic corrections and using realistic $ \pi K $ interactions. These are obtained from a dispersive analysis of scattering data, which provides an accurate and model-independent description of the $ \kappa/K^*_0(700) $ resonance pole. The chiral symmetry suppression of the $ \pi K $ interactions at low energies and the non-ordinary features of the $ \kappa/K^*_0(700) $ seem to suggest that the $ \pi^+ K_S $ source radius might be surprisingly smaller than for other hadronic processes when using the standard and simple Lednicky-Lyuboshits factorization approximation.

Figures

Figures reproduced from arXiv: 2501.11408 by the authors.

**Figure 1.** 𝐾𝜋 scattering data in the scalar channel 𝐾 +𝜋 − (Aston [8] in open square markers, Estabrooks [9] in filled circular markers). The scalar channel amplitude is defined as ˆ𝑓𝑆 ≡ ˆ𝑓 1/2 0 + ˆ𝑓 3/2 0 /2 = | ˆ𝑓𝑆 | exp (𝑖𝜙𝑆). Top: | ˆ𝑓𝑆 |, Bottom: 𝜙𝑆. The red line is the BW used by ALICE (Fit 1. The other two are similar). Blue lines correspond to the dispersive analysis of [13]. Dashed lines are obtained ignoring the 𝐼 =… view at source ↗

**Figure 2.** The blue curve is the result of ALICE (fit 1, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Our preliminary description of femtoscopic s-wave correlations for the 3 ALICE datasets [4]. The red lines and bands are the results of our fits using our formalism with realistic 𝐾𝜋 interactions and relativistic corrections. 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. 5 [PITH_FULL_IMAGE… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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M. A. Lisa, S. Pratt, R. Soltz, and U. Wiedemann, Ann. Rev. Nucl. Part. Sci.55, 357 (2005), arXiv:nucl-ex/0505014

arXiv 2005

[2] [2]

Fabbietti, V

L. Fabbietti, V. Mantovani Sarti, and O. Vazquez Doce, Ann. Rev. Nucl. Part. Sci.71, 377 (2021), arXiv:2012.09806 [nucl-ex]

arXiv 2021

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Acharyaet al

S. Acharyaet al. (ALICE), Phys. Lett. B833, 137335 (2022), arXiv:2111.06611 [nucl-ex]

arXiv 2022

[4] [4]

Acharyaet al

S. Acharyaet al. (ALICE), Phys. Lett. B856, 138915 (2024), arXiv:2312.12830 [hep-ex]

arXiv 2024

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S. E. Koonin, Phys. Lett. B70, 43 (1977)

1977

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Pratt, Phys

S. Pratt, Phys. Rev. Lett.53, 1219 (1984)

work page 1984

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Lednicky and V

R. Lednicky and V. L. Lyuboshits, Yad. Fiz.35, 1316 (1981)

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