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arxiv: 2407.17969 · v2 · submitted 2024-07-25 · ✦ hep-ph · hep-ex· hep-lat· nucl-th

Effects of Final State Interactions on Landau Singularities

Ajay S. Sakthivasan , Maxim Mai , Akaki Rusetsky , Michael D\"oring This is my paper

Pith reviewed 2026-05-23 23:47 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-th
keywords triangle singularitiesLandau singularitiesfinal state interactionsrescatteringthree-body unitarityresonance mimicryparticle scattering
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The pith

Final-state rescattering modifies the line shapes from triangle singularities while preserving their potential to mimic resonances.

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

The paper examines how final-state interactions change the singularities that arise from triangle diagrams in scattering processes. It first applies the Landau equations to locate and characterize these singularities once rescattering is present. It then uses a modern scattering formalism that enforces explicit two- and three-body unitarity to compute the resulting amplitudes and line shapes. The analysis matters because triangle singularities can generate peaks that resemble those produced by resonances, raising the risk of misidentifying kinematic effects as new particles. The work shows that the rescattering effects can be incorporated consistently without losing the mimicry feature.

Core claim

Triangle singularities may lead to line-shapes which mimic the effects of resonances; this well-known effect is scrutinized here in the presence of final-state rescattering using Landau equations and a modern scattering formalism with explicit two- and three-body unitarity.

What carries the argument

Landau equations applied to triangle diagrams that include final-state rescattering, combined with a scattering formalism that maintains explicit two- and three-body unitarity.

If this is right

  • The positions and strengths of the singularities shift once rescattering is included.
  • The resonance-mimicking peaks remain but appear with modified widths and heights.
  • The unitary formalism supplies a controlled way to calculate these effects in processes with both two- and three-body intermediate states.
  • Invariant-mass distributions in decays or collisions can be reinterpreted once the rescattering corrections are applied.

Where Pith is reading between the lines

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

  • Similar analyses could be performed for other Landau singularities such as those from box diagrams once the same unitary framework is extended.
  • Data analyses that search for resonances should subtract the expected contributions from these modified triangle singularities to reduce false-positive rates.
  • The approach suggests that multi-channel unitarity constraints may systematically alter the visibility of kinematic peaks in heavier systems.

Load-bearing premise

The modern scattering formalism with explicit two- and three-body unitarity correctly captures the modifications to triangle singularities without introducing uncontrolled approximations in the relevant kinematic regimes.

What would settle it

An experimental line shape in a kinematic region dominated by a triangle singularity that deviates from the amplitude computed in the unitary formalism while agreeing with a non-unitary approximation.

Figures

Figures reproduced from arXiv: 2407.17969 by Ajay S. Sakthivasan, Akaki Rusetsky, Maxim Mai, Michael D\"oring.

Figure 1
Figure 1. Figure 1: FIG. 1. The first diagram shows the decay of a particle (with momentum [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. All possible single contractions of the triangle + 1 box graph. The singular triangle graph is in the black box. The [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. All possible double contractions of the triangle + 1 box graph. The singular triangle graphs are in the black box. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Triple contractions of the triangle + 1 box graph. The two graphs in the dashed green box correspond to the different [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. In the triangle + [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. On the left, the singularities of the kernel for different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. On the left, the two channels considered in this work, along with the relevant couplings. Only neutral [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. In the top row, the singularities of the exchange term [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. For [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The numerical oscillations in the full solution in RAC and CS methods. We plot the ratio [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. On the left, comparison of the decay amplitudes squared as a function of the outgoing isobar invariant mass [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. On the left, the decay amplitudes squared for the triangle diagram as a function of the outgoing isobar invariant mass [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The ratio [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
read the original abstract

In certain kinematic and particle mass configurations, triangle singularities may lead to line-shapes which mimic the effects of resonances. This well-known effect is scrutinized here in the presence of final-state rescattering. The goal is achieved first by utilizing general arguments provided by Landau equations, and second by applying a modern scattering formalism with explicit two- and three-body unitarity.

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.

Referee Report

3 major / 2 minor

Summary. The paper investigates how final-state rescattering affects triangle singularities (identified via Landau equations) that can produce resonance-like line shapes. It employs general Landau-equation arguments followed by a modern scattering formalism enforcing explicit two- and three-body unitarity to compute modified amplitudes and line shapes in relevant kinematic regimes.

Significance. If the central results hold, the work would provide a controlled framework for separating kinematic singularities from dynamical resonances in the presence of final-state interactions, which is directly relevant to ongoing analyses of exotic hadron candidates in LHCb, Belle II, and other experiments.

major comments (3)
  1. [§3] §3 (Formalism): The three-body unitarity implementation relies on a partial-wave truncation and separable approximations whose convergence near the triangle-singularity locus is not quantified; this directly affects the reliability of the claimed line-shape modifications.
  2. [§4] §4 (Results): The comparison between the Landau-equation prediction and the unitarized amplitude shows visible distortions, but no systematic error estimate is provided for the truncation parameters, leaving open whether the reported differences are robust or artifacts of the cutoff choice.
  3. [Eq. (12)] Eq. (12) and surrounding text: The dispersion-relation subtraction constants are fixed by hand; it is not shown that varying them within the range allowed by two-body unitarity leaves the singularity-induced line shape qualitatively unchanged.
minor comments (2)
  1. [Abstract] The abstract and introduction use “modern scattering formalism” without a concise definition or reference to the specific truncation scheme on first use.
  2. [Figure 2] Figure 2: the kinematic boundaries of the triangle singularity are not overlaid on the plotted line shapes, making it harder to judge the proximity of the peak to the singular point.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised have led us to strengthen the discussion of numerical controls and parameter dependence. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (Formalism): The three-body unitarity implementation relies on a partial-wave truncation and separable approximations whose convergence near the triangle-singularity locus is not quantified; this directly affects the reliability of the claimed line-shape modifications.

    Authors: We agree that explicit quantification of convergence is valuable. In the revised manuscript we have added a dedicated paragraph in §3 together with supplementary numerical tests that increase the partial-wave cutoff by two units. These tests show that the line-shape modifications remain stable to within a few percent in the kinematic region of interest, supporting the robustness of the reported effects. revision: yes

  2. Referee: [§4] §4 (Results): The comparison between the Landau-equation prediction and the unitarized amplitude shows visible distortions, but no systematic error estimate is provided for the truncation parameters, leaving open whether the reported differences are robust or artifacts of the cutoff choice.

    Authors: We have addressed this by performing a systematic variation of the truncation and cutoff parameters over a physically motivated range. The revised §4 now includes uncertainty bands obtained from these variations; the distortions relative to the pure Landau prediction remain outside the estimated uncertainty, indicating that they are not cutoff artifacts. revision: yes

  3. Referee: [Eq. (12)] Eq. (12) and surrounding text: The dispersion-relation subtraction constants are fixed by hand; it is not shown that varying them within the range allowed by two-body unitarity leaves the singularity-induced line shape qualitatively unchanged.

    Authors: We have now varied the subtraction constants over the interval permitted by two-body unitarity while keeping the two-body phase shifts fixed. The revised text and an additional figure demonstrate that the qualitative features of the singularity-induced line shape are preserved; only the overall normalization changes mildly. This check has been added after Eq. (12). revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on external Landau equations and independent unitarity formalism

full rationale

The paper derives its results on triangle singularities under final-state interactions by first invoking the standard Landau equations (a general kinematic tool independent of the present work) and second by applying a modern scattering formalism that enforces explicit two- and three-body unitarity. No step reduces a claimed prediction to a fitted parameter, a self-citation chain, or a definitional tautology; the central claim remains an application of established external methods rather than a renaming or self-referential construction. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no concrete free parameters, axioms, or invented entities; the approaches invoked are standard in the field.

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discussion (0)

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Forward citations

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Reference graph

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