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arxiv: 2606.18652 · v1 · pith:OJN45PHOnew · submitted 2026-06-17 · ✦ hep-ph

Semi-invisible Hyperon Decays in the Effective Lagrangian Approach

Lai Jiang , Ye Xing , Yu Zhou , Xiao-hui Hu This is my paper

Pith reviewed 2026-06-26 20:43 UTC · model grok-4.3

classification ✦ hep-ph
keywords hyperon decayssemi-invisible decayseffective Lagrangianbranching ratiosMesogenesistriangle diagramsfinal-state interactions
0
0 comments X

The pith

Effective Lagrangian calculations predict branching ratios of order 10^{-5} for several hyperon decays to a pion plus an invisible particle.

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

The paper examines semi-invisible hyperon decays of the form hyperon to pion or photon plus an invisible particle ψ within the Mesogenesis mechanism. It employs an effective Lagrangian to compute both tree-level amplitudes and one-loop contributions arising from triangle diagrams that incorporate final-state interactions. These loop effects prove comparable in magnitude to the tree diagrams for multiple channels and cannot be neglected in cases such as Σ⁻ to π⁻ ψ and Ξ⁰ to π⁰ ψ. The resulting branching ratios for the hadronic modes reach order 10^{-5} in particular for Σ⁺ to π⁺ ψ, Ξ⁰ to π⁰ ψ, and Ξ⁻ to π⁻ ψ, while the radiative modes stay below 10^{-7}.

Core claim

In the Mesogenesis mechanism, the branching ratios of hyperon hadronic semi-invisible decays are found to be of order 10^{-5}, particularly for Σ⁺→π⁺ψ, Ξ⁰→π⁰ψ, and Ξ⁻→π⁻ψ, whereas those of radiative semi-invisible decays are less than 10^{-7}. The one-loop hadronic contribution of triangle diagrams with final-state interactions yields sizable corrections that are as significant as those from tree diagrams, especially for Σ⁻→π⁻ψ and Ξ⁰→π⁰ψ.

What carries the argument

Effective Lagrangian approach with one-loop triangle diagrams that include final-state interactions.

If this is right

  • The channels Σ⁺→π⁺ψ, Ξ⁰→π⁰ψ, and Ξ⁻→π⁻ψ are expected to have the largest observable rates among the hadronic modes.
  • Radiative semi-invisible decays remain suppressed by at least two orders of magnitude relative to the hadronic ones.
  • Loop contributions must be retained to obtain reliable predictions for Σ⁻→π⁻ψ and Ξ⁰→π⁰ψ.
  • These rates arise directly from the combination of tree and one-loop amplitudes in the chosen effective Lagrangian.

Where Pith is reading between the lines

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

  • Confirmation of these rates would offer a concrete experimental handle on the invisible particle ψ in the Mesogenesis picture.
  • Similar loop-corrected calculations could be extended to other baryon species or to related invisible-particle scenarios.
  • Current hyperon production experiments could set meaningful limits on the predicted channels with modest improvements in sensitivity.
  • Discrepancies between measured and predicted rates would point to the need for additional interaction terms beyond the triangle diagrams.

Load-bearing premise

The effective Lagrangian and the specific triangle-diagram contributions with final-state interactions accurately represent the hadronic physics without large higher-order or non-perturbative effects that would change the numerical results.

What would settle it

An experimental upper limit or measured value for the branching ratio of Σ⁺→π⁺ψ that lies well below or above 10^{-5} would contradict the central prediction.

Figures

Figures reproduced from arXiv: 2606.18652 by Lai Jiang, Xiao-Hui Hu, Ye Xing, Yu Zhou.

Figure 1
Figure 1. Figure 1: FIG. 1: The possible Feynman diagrams for the semi-invisible hyperon [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The tree and triangle diagrams of semi-invisible hyperon deca [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The leading order radiative semi-invisible decay of hyperons is [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The branching ratios of the hadronic semi-invisible modes (left [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Dependence of branching ratios on [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

We systematically investigate the semi-invisible decays of hyperons (hyperon $\to \pi(/\gamma)\ +$ invisible($\psi$)) in the Mesogenesis mechanism by the effective Lagrangian approach. The one-loop hadronic contribution of triangle diagrams with final-state interactions is fully examined in the present work. Our analysis indicates that the triangle diagram yield sizable corrections to the branching ratio that are as significant as those from tree diagrams. Especially for the $\Sigma^-\to \pi^-\psi$ and $\Xi^0 \to \pi^0 \psi$, their loop contributions cannot be ignored. Consequently, the branching ratios of hyperon hadronic semi-invisible decays are found to be of order $10^{-5}$, particularly for $\Sigma^+\to\pi^+\psi$, $\Xi^0\to\pi^0\psi$, and $\Xi^-\to\pi^-\psi$, whereas those of radiative semi-invisible decays are less than $10^{-7}$.

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

2 major / 1 minor

Summary. The manuscript systematically investigates semi-invisible hyperon decays (hyperon → π(γ) + invisible ψ) in the Mesogenesis mechanism within the effective Lagrangian approach. It computes tree-level amplitudes together with one-loop contributions from triangle diagrams that incorporate final-state interactions, concluding that the loop terms are sizable and comparable in magnitude to the tree-level contributions (especially for Σ⁻ → π⁻ψ and Ξ⁰ → π⁰ψ). This leads to predicted branching ratios of order 10^{-5} for several hadronic modes (notably Σ⁺ → π⁺ψ, Ξ⁰ → π⁰ψ, Ξ⁻ → π⁻ψ) while radiative modes remain below 10^{-7}.

Significance. If the numerical results prove robust, the work supplies concrete, testable predictions for rare hyperon decays that could probe the Mesogenesis scenario. The explicit inclusion and size assessment of loop diagrams with final-state interactions is a positive feature that draws attention to an often-neglected class of contributions in effective-theory calculations of hyperon processes.

major comments (2)
  1. [Loop calculation (Sec. 3) and numerical results] The headline result that loop contributions are 'as significant as those from tree diagrams' and drive BR ~ 10^{-5} rests on the triangle-diagram integrals. No variation of the ultraviolet cutoff, regularization scheme, or form-factor suppression is reported for these integrals at the ~1 GeV momentum transfers characteristic of hyperon decays; without such a sensitivity study the order-of-magnitude claim remains vulnerable to uncontrolled hadronic-scale uncertainties.
  2. [Effective Lagrangian setup and results section] The effective-Lagrangian couplings are standardly determined from other processes; the manuscript does not demonstrate that the quoted branching ratios constitute independent predictions rather than being largely fixed by those external inputs (cf. the circularity concern for the numerical outputs).
minor comments (1)
  1. [Abstract] The abstract states results to order-of-magnitude precision but supplies neither explicit parameter values nor error estimates; adding a short table of central values with estimated theoretical ranges would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment below, providing clarifications and indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Loop calculation (Sec. 3) and numerical results] The headline result that loop contributions are 'as significant as those from tree diagrams' and drive BR ~ 10^{-5} rests on the triangle-diagram integrals. No variation of the ultraviolet cutoff, regularization scheme, or form-factor suppression is reported for these integrals at the ~1 GeV momentum transfers characteristic of hyperon decays; without such a sensitivity study the order-of-magnitude claim remains vulnerable to uncontrolled hadronic-scale uncertainties.

    Authors: We acknowledge the importance of assessing sensitivity to the regularization procedure. The triangle integrals are computed in dimensional regularization supplemented by a hard cutoff at the hadronic scale (~1 GeV) to tame the ultraviolet divergence, with dipole form factors taken from standard parametrizations fitted to hyperon data. In the revised version we will add an explicit sensitivity study varying the cutoff between 0.8 and 1.5 GeV and comparing results obtained with a Pauli-Villars regulator; this will quantify the hadronic uncertainty and strengthen the robustness claim for the order-of-magnitude branching ratios. revision: yes

  2. Referee: [Effective Lagrangian setup and results section] The effective-Lagrangian couplings are standardly determined from other processes; the manuscript does not demonstrate that the quoted branching ratios constitute independent predictions rather than being largely fixed by those external inputs (cf. the circularity concern for the numerical outputs).

    Authors: The hadronic couplings (e.g., those entering the tree-level and loop vertices) are fixed from measured non-leptonic hyperon decays, as is standard in effective-theory analyses. The new-physics couplings involving the invisible ψ, however, are independent parameters of the Mesogenesis scenario and are not constrained by existing data. The computed branching ratios therefore constitute genuine predictions for the semi-invisible channels. We will insert a clarifying paragraph in Sec. 2 and the results section to explicitly separate the externally fixed hadronic parameters from the new-physics couplings, thereby addressing the circularity concern. revision: partial

Circularity Check

0 steps flagged

No significant circularity; branching ratios are model predictions from external inputs

full rationale

The derivation applies an effective Lagrangian to compute tree and one-loop contributions to hyperon semi-invisible decay branching ratios. Inputs are standard couplings and form factors drawn from other processes; the outputs are new numerical results for the target modes. No equations or self-citations reduce the claimed BR values to tautological redefinitions or refits of the same quantities. The calculation is therefore a standard model application rather than a closed loop on its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit list of fitted couplings or invented entities; typical effective-Lagrangian analyses introduce several free parameters for meson-baryon couplings and form factors whose values are taken from external fits.

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discussion (0)

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