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arxiv: 2606.04630 · v1 · pith:HGDJQSRUnew · submitted 2026-06-03 · ✦ hep-ph

Study of Λ⁰_b to Λ D decays with the rescattering mechanism

Na Li , Hui-Qiang Shang , Qin Qin This is my paper

Pith reviewed 2026-06-28 05:44 UTC · model grok-4.3

classification ✦ hep-ph
keywords Lambda_b decaysfinal-state rescatteringCP violationbranching fractionsnon-leptonic decaysD mesonsLHCb predictions
0
0 comments X

The pith

Rescattering boosts the anti-D0 Lambda branching fraction by two orders of magnitude while supplying strong phases for CP violation.

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

The paper examines non-leptonic decays of the Lambda_b baryon to Lambda and D mesons by combining short-distance factorizable amplitudes with long-distance effects from hadronic triangle rescattering diagrams. It establishes that these rescattering terms are required both to generate the strong phases that enable observable CP violation and to increase the rate of the anti-D0 channel by a factor of roughly one hundred. Branching ratios are computed for different partial waves, and direct CP asymmetries reach sizable values in the charged D channels. The results supply concrete predictions that can be compared with data from the LHCb experiment to sharpen the extraction of the CKM angle gamma.

Core claim

The framework integrates short-distance factorizable amplitudes with long-distance non-factorizable contributions arising from hadronic triangle rescattering diagrams. The final-state rescattering contributions are essential, not only because they provide the strong phases necessary for CP violation, but also because they enhance the anti-D0 Lambda branching fraction by two orders of magnitude. Numerically, the branching ratios of the channels with different partial waves are calculated, as well as the corresponding CP-violating observables, with direct CP asymmetries a_CP^dir(D+) = 0.28 and a_CP^dir(D-) = -0.14 found to be very significant.

What carries the argument

Hadronic triangle rescattering diagrams, integrated with short-distance factorizable amplitudes to capture the dominant long-distance non-factorizable contributions.

If this is right

  • Branching ratios are obtained for the decays in different partial waves.
  • Direct CP asymmetries reach 0.28 in the D+ channel and -0.14 in the D- channel.
  • The results supply a theoretical benchmark that can be tested at the LHCb experiment.
  • Rescattering is required both to produce the phases for CP violation and to raise the anti-D0 rate by two orders of magnitude.

Where Pith is reading between the lines

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

  • The same rescattering treatment could be applied to other baryon-to-baryon-plus-meson decays where factorizable amplitudes alone underpredict rates.
  • Confirmation of the large enhancement would indicate that omitting triangle diagrams in similar processes systematically underestimates branching fractions by large factors.
  • Measurements that separate partial-wave contributions could provide a direct test of how the rescattering amplitudes are modeled.

Load-bearing premise

The model assumes that hadronic triangle rescattering diagrams can be reliably integrated with short-distance factorizable amplitudes to capture the dominant long-distance non-factorizable contributions without additional uncontrolled effects.

What would settle it

An experimental measurement of the Lambda_b to Lambda anti-D0 branching fraction that remains close to the small factorizable prediction, or direct CP asymmetries inconsistent with the calculated values around 0.28 and -0.14, would show that the rescattering contributions are not essential.

Figures

Figures reproduced from arXiv: 2606.04630 by Hui-Qiang Shang, Na Li, Qin Qin.

Figure 1
Figure 1. Figure 1: FIG. 1: Quark-level tree diagrams for [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Hadronic triangle diagrams and kinematic notations for the final-state rescattering contributions to [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The dependence of the predicted branching fractions (left panel) and direct [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

We employ the final-state rescattering mechanism to systematically investigate the non-leptonic decays $\Lambda_b^0 \to \Lambda D$ (where $D = D^0$, $\overline{D}^0$, $D_+$, $D_-$), which can help improve the experimental precision of the $CP$-violating phase angle $\gamma$. The framework integrates short-distance factorizable amplitudes with long-distance non-factorizable contributions arising from hadronic triangle rescattering diagrams. We find that the final-state rescattering contributions are essential, not only because they provide the strong phases necessary for $CP$ violation, but also because they enhance the $\overline{D}^0 \Lambda$ branching fraction by two orders of magnitude. Numerically, we calculate the branching ratios of the channels with different partial waves, as well as the corresponding $CP$-violating observables. In particular, the direct $CP$ asymmetries $a_{CP}^{\mathrm{dir}}(D_+) = 0.28^{+0.07}_{-0.11}$ and $a_{CP}^{\mathrm{dir}}(D_-) = -0.14^{+0.06}_{-0.04}$ are found to be very significant. These results provide a reliable theoretical benchmark and can be tested against future measurements from the LHCb experiment.

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 paper employs the final-state rescattering mechanism to study non-leptonic decays Λ_b^0 → Λ D (D = D^0, ar D^0, D^+, D^-). It combines short-distance factorizable amplitudes with long-distance contributions from hadronic triangle rescattering diagrams, concluding that rescattering provides essential strong phases for CP violation and enhances the ar D^0 Λ branching fraction by two orders of magnitude. Numerical results are given for branching ratios in different partial waves and CP-violating observables, with specific values such as a_CP^dir(D_+) = 0.28^{+0.07}_{-0.11} and a_CP^dir(D_-) = -0.14^{+0.06}_{-0.04}.

Significance. If the rescattering contributions can be reliably computed, the results supply testable predictions for CP asymmetries in baryon decays that may help constrain the CKM angle γ at LHCb and underscore the role of non-factorizable long-distance effects.

major comments (2)
  1. [Numerical results] The central claim of a two-order-of-magnitude enhancement in BR(ar D^0 Λ) rests on the hadronic triangle rescattering amplitudes; the manuscript provides no systematic variation of vertex couplings, form-factor choices, or loop regularization (cutoff or dispersion relations) to demonstrate stability of this result.
  2. [Abstract] The reported CP asymmetries and branching ratios are presented as numerical benchmarks, yet the abstract and main text give no derivation details, error propagation from model inputs, or comparison to existing data that would allow assessment of the quoted uncertainties.
minor comments (1)
  1. Clarify in the text how the different partial waves are incorporated into the amplitude construction and whether interference terms are fully accounted for in the CP observables.

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 changes planned for the revised version.

read point-by-point responses

  1. Referee: [Numerical results] The central claim of a two-order-of-magnitude enhancement in BR(\bar D^0 Λ) rests on the hadronic triangle rescattering amplitudes; the manuscript provides no systematic variation of vertex couplings, form-factor choices, or loop regularization (cutoff or dispersion relations) to demonstrate stability of this result.

    Authors: The couplings and form factors are fixed to values taken from the literature on related processes to maintain consistency across the calculation. A complete scan over all possible variations is computationally demanding. We will nevertheless add in the revision a limited sensitivity study by varying the cutoff parameter in the range 1.0–1.5 GeV and by employing an alternative monopole form-factor parametrization; the results will be presented in a new table or figure to illustrate that the two-order enhancement persists under these changes. revision: partial

  2. Referee: [Abstract] The reported CP asymmetries and branching ratios are presented as numerical benchmarks, yet the abstract and main text give no derivation details, error propagation from model inputs, or comparison to existing data that would allow assessment of the quoted uncertainties.

    Authors: The abstract is intentionally concise; the full amplitude construction, including factorization and the triangle rescattering diagrams, is derived in Sections 2 and 3. The quoted uncertainties on a_CP^dir arise from the CKM elements and the dominant hadronic inputs. We agree that an explicit propagation discussion is useful and will insert a dedicated subsection summarizing the main sources of theoretical uncertainty and their effect on the observables. Because no experimental data yet exist for these channels, the manuscript already frames the numbers as predictions for LHCb; this point will be reinforced. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context describe a phenomenological framework combining short-distance factorizable amplitudes with long-distance hadronic triangle rescattering diagrams to compute branching ratios and CP asymmetries. No equations, self-citations, or parameter-fitting steps are quoted that would reduce the claimed two-order enhancement or CP values to inputs by construction. The numerical results are presented as outputs of the integrated model rather than tautological renamings or fitted-input predictions. The derivation chain appears self-contained against external benchmarks with no load-bearing self-citation or ansatz smuggling evident.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; specific free parameters, axioms, and invented entities cannot be extracted without the full text. The approach relies on an unstated model for triangle rescattering diagrams and matching to short-distance amplitudes.

pith-pipeline@v0.9.1-grok · 5769 in / 1074 out tokens · 31179 ms · 2026-06-28T05:44:46.500095+00:00 · methodology

discussion (0)

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