arxiv: 2603.02979 · v2 · submitted 2026-03-03 · ✦ hep-ph · nucl-th

Recognition: 2 theorem links

· Lean Theorem

Scattering and Femtoscopic Correlation Functions of the Sigma_c⁺⁺π⁺, Sigma_c⁰π⁻ and Sigma_b⁺π⁺ Systems

Mikel F. Barbat , Juan Nieves , Laura Tolos

Authors on Pith no claims yet

Pith reviewed 2026-05-15 17:02 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords femtoscopic correlation functionsSigma_c pi scatteringI=2 isotensor channelCoulomb effectsheavy quark symmetryscattering lengthLambda_c(2595)

0 comments

The pith

The Σ_c⁰π⁻ femtoscopic correlation function is the most suitable observable for constraining the strong dynamics of the isotensor Σ_cπ system.

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

This paper calculates scattering lengths, effective ranges, and femtoscopic correlation functions for the I=2 Σ_c^{++}π⁺, Σ_c⁰π⁻, and Σ_b⁺π⁺ systems. Two models of the strong interaction are employed, each constrained only by reproducing the known isoscalar resonances Λ_c(2595) and Λ_b(5912). The neutral Σ_c⁰π⁻ channel is governed solely by the strong force, while charged channels include relativistic Coulomb contributions. Model differences trace mainly to choices of ultraviolet regularization. Heavy-quark flavor symmetry produces similar global patterns in the charm and bottom correlation functions. A reader would care because these functions offer a route to test low-energy hadron interactions through measurements in heavy-ion collisions where direct scattering data remain scarce.

Core claim

The authors formulate the strong interaction within two distinct frameworks constrained to reproduce the lowest-lying odd-parity isoscalar spin-1/2 resonances. They compute scattering observables and femtoscopic correlation functions, adding relativistic Coulomb wave functions for charged pairs. Differences between the models in scattering observables arise mainly from the specific ultraviolet regularization schemes. Coulomb effects produce only a very small increase in both the scattering length and the effective range. The resulting correlation functions display analogous global features in the charm and bottom sectors. Strong-interaction-only calculations of the correlation functions show

What carries the argument

Two strong-interaction frameworks constrained to reproduce the Λ_c(2595) and Λ_b(5912) resonances, with femtoscopic correlation functions evaluated using relativistic Coulomb wave functions for charged pairs.

If this is right

Differences observed in scattering observables between the two models originate primarily from their distinct ultraviolet regularization schemes.
Inclusion of Coulomb effects induces only a very small increase in both the scattering length and the effective range.
The correlation functions in the charm and bottom sectors exhibit analogous global features consistent with heavy-quark flavor symmetry.
The Σ_c^{++}π⁺ and Σ_b⁺π⁺ correlation functions lose most of their ability to discriminate between models once Coulomb repulsion is included.
The neutral Σ_c⁰π⁻ correlation function, free from Coulomb effects, retains the highest sensitivity to the details of the underlying strong dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Future femtoscopic measurements focused on the neutral Σ_c⁰π⁻ pair could directly test which ultraviolet regularization scheme better describes the I=2 channel.
The modest size of Coulomb corrections suggests that strong-interaction signals in other charged hadron pairs may remain accessible if electrostatic contributions can be subtracted reliably.
Heavy-quark symmetry relations established here could be used to predict correlation functions for additional bottom-sector channels once the charm-sector results are validated.

Load-bearing premise

The two strong-interaction models are constrained solely by reproducing the known isoscalar resonances, without independent validation of their ultraviolet regularization schemes in the isotensor I=2 channels.

What would settle it

A measurement of the Σ_c⁰π⁻ femtoscopic correlation function in heavy-ion collisions that matches one model's prediction but deviates from the other's would confirm the discriminating power of the neutral channel.

Figures

Figures reproduced from arXiv: 2603.02979 by Juan Nieves, Laura Tolos, Mikel F. Barbat.

**Figure 2.** Figure 2: FIG. 2. Strong isotensor Σ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Σ [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. The same CFs for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Strong isotensor Σ [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Σ [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. The same as is Fig [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

read the original abstract

We present predictions for scattering observables and femtoscopic correlation functions (CFs) of the $I=2$ $\Sigma_c^{++}\pi^{+}$, $\Sigma_c^{0}\pi^{-}$ systems and its heavy-flavor counterpart $\Sigma_b^{+}\pi^{+}$. In both heavy-quark sectors, the strong interaction is formulated within two distinct theoretical frameworks, each constrained to reproduce the lowest-lying odd-parity isoscalar spin-$1/2$ resonances, $\Lambda_c(2595)$ and $\Lambda_b(5912)$, respectively. While the $\Sigma_c^{0}\pi^{-}$ pair is governed solely by the strong interaction, electrostatic contributions are included in the other two channels involving charged particles through relativistic Coulomb wave functions. We show that the differences observed in the scattering observables between the two strong-interaction models arise mainly from the specific ultraviolet regularization schemes employed. The inclusion of Coulomb effects induces only a very small increase in both the scattering length and the effective range. The resulting CFs in the charm and bottom sectors display analogous global features, in agreement with expectations from heavy-quark flavor symmetry. Both, the $\Sigma_c^{++}\pi^+$ and $\Sigma_b^{+}\pi^{+}$ CFs, when computed including only the strong interaction, exhibits substantial discriminating power among the different models. However, once Coulomb effects are incorporated, the CFs become largely affected by the repulsive electrostatic interaction, which diminishes their sensitivity to the details of the underlying strong dynamics, thereby reducing the capability to differentiate between theoretical descriptions. Thus, the $\Sigma_c^{0}\pi^{-}$ CF-being free from Coulomb effects-provides the most suitable observable for constraining the strong dynamics of the isotensor $\Sigma_c\pi$ system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper supplies explicit numerical predictions for scattering lengths, effective ranges, and femtoscopic correlation functions in the I=2 Σ_c π and Σ_b π systems using two existing models, with the neutral channel emerging as the cleanest observable.

read the letter

The main takeaway is that the authors apply two standard frameworks already tuned to the Λ_c(2595) and Λ_b(5912) to compute I=2 observables for Σ_c^{++}π^+, Σ_c^0π^-, and Σ_b^+π^+. They add relativistic Coulomb wave functions for the charged pairs and show that the resulting correlation functions look similar across charm and bottom sectors, consistent with heavy-quark symmetry expectations. The neutral channel avoids Coulomb repulsion, so its correlation function retains more sensitivity to the underlying strong dynamics while the charged ones get washed out by electrostatic effects. The calculations are straightforward and the differences between models are traced mainly to their ultraviolet regularization choices, which the paper itself flags as the source of spread in the scattering lengths and effective ranges. What works is the clean separation of strong and electromagnetic pieces and the direct numerical output that experimental groups could compare to heavy-ion data. The soft spot is that both frameworks are fixed solely by the I=0 resonances, with no independent lattice datum or other constraint applied to the isotensor channel. The spread in predictions therefore mixes possible physics differences with scheme dependence, which limits how strongly one can claim the neutral correlation function will discriminate models. The formalism and citations are standard for this corner of effective theory, with no internal contradictions. This is useful for people running femtoscopy analyses in heavy-flavor collisions who need concrete numbers to test against. It deserves peer review because the predictions are explicit and falsifiable even if the model dependence requires more discussion in revision.

Referee Report

2 major / 3 minor

Summary. The paper presents predictions for scattering observables (lengths and effective ranges) and femtoscopic correlation functions for the I=2 Σ_c^{++}π^+, Σ_c^0π^-, and Σ_b^+π^+ systems. Two distinct strong-interaction frameworks are employed, each constrained only by reproducing the lowest-lying odd-parity isoscalar resonances Λ_c(2595) and Λ_b(5912). Relativistic Coulomb wave functions are added for the charged channels. Differences between models are attributed primarily to ultraviolet regularization schemes. The analysis concludes that the neutral Σ_c^0π^- correlation function, free of Coulomb effects, offers the greatest sensitivity to the underlying strong dynamics, while Coulomb repulsion in the charged channels reduces model-discriminating power.

Significance. If the central results hold, the work supplies concrete, testable predictions for correlation functions in the charm and bottom sectors that can guide femtoscopic analyses at the LHC. It quantifies the impact of Coulomb interactions on observable sensitivity and illustrates heavy-quark flavor symmetry expectations between charm and bottom sectors. The explicit comparison of two regularization schemes usefully exposes a source of theoretical uncertainty in I=2 predictions.

major comments (2)

[Section 3] Section 3: Both frameworks are constrained solely by fitting to the I=0 resonances Λ_c(2595) and Λ_b(5912). No lattice datum, sum-rule constraint, or other I=2 observable is used to fix or cross-check the ultraviolet regularization parameters. Consequently, the reported differences in I=2 scattering lengths and effective ranges (Table 2) may reflect scheme dependence rather than robust strong-interaction physics; this assumption is load-bearing for the claim that the neutral CF possesses substantial discriminating power among models.
[Section 5.3] Section 5.3 and Figure 5: The conclusion that Coulomb effects 'diminish their sensitivity' and thereby reduce the capability to differentiate models is illustrated qualitatively by the CF plots. A quantitative measure (e.g., the ratio of model-to-model variation with versus without Coulomb, or a χ² distinguishability metric at low q) is needed to substantiate that the neutral channel is unambiguously 'the most suitable' observable.

minor comments (3)

[Abstract] The abstract and Section 1 refer to 'its heavy-flavor counterpart' for the bottom sector; ensure the title and all section headings use consistent notation for the Σ_b^+π^+ system.
[Eq. (8)] Equation (8) defines the correlation function C(q); the text occasionally employs 'CF' without explicitly restating the momentum argument, which could be clarified for readers unfamiliar with femtoscopy conventions.
[Figures 3-4] Figures 3 and 4 would benefit from shaded bands indicating the variation induced by the ultraviolet cutoff range; this would make the model-dependence discussion more transparent.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

Referee: [Section 3] Section 3: Both frameworks are constrained solely by fitting to the I=0 resonances Λ_c(2595) and Λ_b(5912). No lattice datum, sum-rule constraint, or other I=2 observable is used to fix or cross-check the ultraviolet regularization parameters. Consequently, the reported differences in I=2 scattering lengths and effective ranges (Table 2) may reflect scheme dependence rather than robust strong-interaction physics; this assumption is load-bearing for the claim that the neutral CF possesses substantial discriminating power among models.

Authors: We agree with the referee that the models are constrained only by the I=0 resonances, which is a standard approach given the lack of I=2 data. The differences in I=2 observables are indeed due to the different regularization schemes, as stated in the manuscript. This scheme dependence represents the theoretical uncertainty in our predictions. The neutral CF's ability to discriminate is shown by the distinct curves in Figure 5 for the two models. We will add a clarifying statement in Section 3 emphasizing that these are extrapolations and the spread indicates model uncertainty. revision: partial
Referee: [Section 5.3] Section 5.3 and Figure 5: The conclusion that Coulomb effects 'diminish their sensitivity' and thereby reduce the capability to differentiate models is illustrated qualitatively by the CF plots. A quantitative measure (e.g., the ratio of model-to-model variation with versus without Coulomb, or a χ² distinguishability metric at low q) is needed to substantiate that the neutral channel is unambiguously 'the most suitable' observable.

Authors: We accept that the current discussion is qualitative and will enhance it with a quantitative measure. Specifically, we will calculate the relative variation between the two models in the correlation function at small q (e.g., the difference in C(q) at q=0 or integrated over low q) for the cases with and without Coulomb. This will be included in Section 5.3 to support the conclusion that the neutral channel is the most suitable. revision: yes

Circularity Check

0 steps flagged

No significant circularity: I=2 predictions independent of I=0 resonance fits

full rationale

The two frameworks are constrained exclusively by reproducing the external I=0 resonances Λ_c(2595) and Λ_b(5912). Scattering lengths, effective ranges, and CFs for the I=2 channels are then computed as genuine predictions. Differences between models are attributed to distinct UV regularization schemes, but these schemes are not fitted to the I=2 observables themselves, nor do any reported quantities reduce to the resonance inputs by algebraic construction. No self-citation load-bearing steps, uniqueness theorems, or ansatz smuggling are present in the derivation chain. The claim that the neutral Σ_c⁰π⁻ CF is Coulomb-free follows directly from electrostatics and is not circular.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on two effective-theory frameworks whose parameters are fixed by resonance data, plus standard relativistic Coulomb wave functions; no new particles or forces are introduced.

free parameters (1)

ultraviolet regularization parameters
Different cutoff schemes in the two models produce the reported differences in scattering observables; these parameters are chosen to reproduce the input resonances.

axioms (2)

domain assumption Heavy-quark flavor symmetry relates the charm and bottom sectors at leading order
Invoked to explain analogous global features of the CFs in the two sectors.
standard math Relativistic Coulomb wave functions correctly capture electrostatic contributions for charged pairs
Standard treatment used without further derivation.

pith-pipeline@v0.9.0 · 5637 in / 1443 out tokens · 44764 ms · 2026-05-15T17:02:01.044066+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the differences observed in the scattering observables between the two strong-interaction models arise mainly from the specific ultraviolet regularization schemes employed... UV cutoff Λ... fixed... by the properties of the odd-parity Λc(2595) resonance
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

both strong-interaction frameworks are constrained solely by reproducing the lowest-lying odd-parity isoscalar spin-1/2 resonances Λc(2595) and Λb(5912)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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