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arxiv: 2604.22867 · v1 · submitted 2026-04-23 · ✦ hep-ph

Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay

Joshua O'Connor This is my paper

Pith reviewed 2026-05-09 20:42 UTC · model grok-4.3

classification ✦ hep-ph
keywords Lorentz violationthree-body decayDalitz plotkinematicsquantum field theoryparticle decaysleading-order effects
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The pith

The kinematics of three-body decays can be analyzed using Dalitz plots modified by leading-order Lorentz violation in quantum field theory.

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

This paper outlines how to incorporate leading-order Lorentz-violating effects into the analysis of three-particle interactions and decays. It focuses on adapting standard kinematic tools for particle physics to account for these violations. A sympathetic reader would care because it provides a way to search for new physics beyond the standard model in decay processes. If the approach holds, experimental data on decay distributions could be reinterpreted to test for Lorentz violation at accessible energies.

Core claim

The paper outlines the analysis of three-particle interactions and decay processes for leading-order modifications in a Lorentz-violating quantum field theory, specifically through the kinematics of Dalitz plots for three-body decays.

What carries the argument

Modified Dalitz plot variables that encode the leading-order effects of Lorentz violation on the momenta and energies in three-body decays.

If this is right

  • Dalitz plots become sensitive to leading-order Lorentz-violating corrections in the decay kinematics.
  • Three-particle interaction analyses must include modified energy-momentum relations at the lowest order in the violation parameters.
  • Decay rates and distributions can be recalculated with these kinematic shifts to compare against data.
  • The method applies directly to any three-body process where Lorentz violation is considered perturbatively.

Where Pith is reading between the lines

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

  • The outlined method could be applied to specific Lorentz-violating models to derive bounds from existing decay data.
  • Similar kinematic adjustments might extend to four-body decays or scattering processes if the leading-order approximation remains valid.
  • This framework connects to tests of Lorentz invariance in other high-energy contexts like neutrino oscillations or cosmic rays.

Load-bearing premise

Leading-order modifications in a Lorentz-violating QFT are sufficient to capture the dominant kinematic effects in three-body decays without higher-order terms or inconsistencies in the underlying theory.

What would settle it

A high-precision measurement of the Dalitz plot for a known three-body decay such as eta to three pions that shows deviations neither explained by standard kinematics nor by the leading-order Lorentz-violating corrections.

Figures

Figures reproduced from arXiv: 2604.22867 by Joshua O'Connor.

Figure 1
Figure 1. Figure 1: Shape of the Dalitz plot for the √ s/m value corresponding to η → 3π 0 . The standard outline is shown, along with outlines for two nonzero values of the Lorentz￾violation parameter cµν. Consider an η meson or kaon as the Lorentz-invariant initial particle, which then decays in the center-of-mass frame into three Lorentz-violating spinless particles of equal mass, such as pions. A compact description of th… view at source ↗
Figure 2
Figure 2. Figure 2: Shape of the Dalitz plot for a √ s/m = 6.5 value. modifications simplifies to Γ = |M|2 512π 2 √ s  s(1 + 2c) + 4cm2 + 4cm2 log  2mc √ s − 2m  . (2) The last term in the expression is recognized as the Lorentz-noninvariant analog of an ultraviolet divergence, with poles at the correct values of the particle mass. Regularization techniques and asymptotic approximations could be further applied to models … view at source ↗
Figure 3
Figure 3. Figure 3: Shape of the Dalitz plot for an ultrarelativistic value of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We outline the analysis of three-particle interactions and decay processes for leading-order modifications in a Lorentz-violating quantum field theory.

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

1 major / 0 minor

Summary. The manuscript outlines an analysis of three-particle interactions and decay processes incorporating leading-order Lorentz-violating modifications in quantum field theory, with emphasis on the resulting Dalitz plot kinematics for three-body decays.

Significance. Lorentz violation effects in decay kinematics could provide testable signatures in high-energy physics if concrete modifications to dispersion relations or phase space are derived. As an outline without explicit results or derivations, the work has limited immediate impact but could serve as a starting point if expanded.

major comments (1)
  1. The manuscript provides no equations, derivations, or sections detailing how leading-order LV modifications alter the dispersion relations, energy-momentum conservation, or Dalitz plot boundaries for the three-body decay. This absence makes it impossible to assess whether the approach yields consistent kinematics or avoids known LV pitfalls such as frame dependence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review of our manuscript. We respond point by point to the major comment below.

read point-by-point responses

  1. Referee: The manuscript provides no equations, derivations, or sections detailing how leading-order LV modifications alter the dispersion relations, energy-momentum conservation, or Dalitz plot boundaries for the three-body decay. This absence makes it impossible to assess whether the approach yields consistent kinematics or avoids known LV pitfalls such as frame dependence.

    Authors: The manuscript is explicitly framed as an outline of the methodological approach for incorporating leading-order Lorentz-violating modifications into the kinematics of three-body decays using Dalitz plots. We acknowledge that the lack of explicit equations and derivations prevents a full evaluation of the resulting kinematics and any potential inconsistencies, such as frame dependence. To address this concern, we will prepare a revised version that includes the leading-order corrections to the dispersion relations, the adjusted four-momentum conservation conditions for the decay, the modified Dalitz plot boundaries, and a discussion of reference-frame choices to mitigate frame-dependence issues. revision: yes

Circularity Check

0 steps flagged

No derivation chain or equations present; paper is purely an outline statement

full rationale

The provided text consists solely of a one-sentence abstract stating an intent to outline analysis of three-particle decays under leading-order Lorentz violation. No equations, dispersion relations, phase-space modifications, Dalitz-plot expressions, or any derivation steps appear. No parameters are fitted, no self-citations are invoked as load-bearing premises, and no predictions are claimed that could reduce to inputs by construction. The absence of any mathematical content means there are no load-bearing steps to inspect for circularity of any enumerated kind. The work is self-contained as a high-level statement of intent and requires no external verification of hidden equivalences.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; full text would be required to populate the ledger.

pith-pipeline@v0.9.0 · 5291 in / 1011 out tokens · 57741 ms · 2026-05-09T20:42:28.544165+00:00 · methodology

discussion (0)

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Reference graph

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