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arxiv: 2505.24338 · v3 · submitted 2025-05-30 · ✦ hep-ph · hep-ex

Implications of the evidence for direct CP violation in Dto π^+π^- decays

Rahul Sinha , Thomas E. Browder , N. G. Deshpande , Dibyakrupa Sahoo , Nita Sinha This is my paper

Pith reviewed 2026-05-19 13:29 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords CP violationD meson decayspenguin amplitudesnew physicscharm physicstopological amplitudesunitarityrescattering
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The pith

Fitted penguin amplitude in D to pi pi decays reaches 4.74 times the tree amplitude, exceeding standard model estimates by more than 3.3 sigma.

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

The paper extracts all topological amplitudes and isospin amplitudes directly from measured observables in D to pi pi decays. This extraction yields a penguin contribution whose central value is 4.74 times the magnitude of the D0 to pi+ pi- amplitude. That fitted size differs from the expected standard-model penguin fraction of roughly 10 percent at a significance above 3.3 sigma. Model-independent unitarity constraints on rescattering amplitudes are used to show that final-state interactions alone cannot generate such a large penguin, implying a contribution from physics beyond the standard model. The authors also demonstrate that a very small new-physics term carrying a large weak phase can resolve the observed discrepancy.

Core claim

By obtaining all topological amplitudes from measured observables for D to pi pi decays, the analysis reveals a penguin amplitude with magnitude 4.74 times that of the D0 to pi+ pi- decay. This central value differs from a reasonable SM estimate of 10% with a significance greater than 3.3 sigma. Model-independent arguments based on unitarity show that large penguins cannot arise from re-scattering alone and likely indicate physics beyond the SM. A very small contribution from physics beyond the SM with a large weak phase can alleviate the problem.

What carries the argument

Topological amplitudes extracted directly from measured observables in D to pi pi decays, together with unitarity constraints on rescattering amplitudes.

If this is right

  • Large penguin contributions in charm decays to two pions cannot be generated by rescattering alone.
  • A small beyond-standard-model amplitude with a large weak phase accounts for the data.
  • Direct CP violation in D to pi pi decays requires new physics.
  • The same amplitude extraction can be applied to related decay channels to test consistency.

Where Pith is reading between the lines

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

  • This result would require revised predictions for CP asymmetries in other charm decay modes.
  • The unitarity argument could be extended to constrain rescattering in bottom-meson decays.
  • Future high-luminosity data could isolate the size and phase of the new-physics contribution.
  • Similar large-penguin signals may appear in related rare charm processes once statistics improve.

Load-bearing premise

The standard-model penguin amplitude is only about 10 percent of the tree amplitude and unitarity of rescattering amplitudes strictly prevents large penguin contributions without new physics.

What would settle it

A higher-precision measurement or independent calculation that finds the penguin amplitude in D to pi pi decays consistent with the 10 percent standard-model expectation would falsify the need for new physics.

Figures

Figures reproduced from arXiv: 2505.24338 by Dibyakrupa Sahoo, N. G. Deshpande, Nita Sinha, Rahul Sinha, Thomas E. Browder.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

The observation of $CP$ violation in the difference of $CP$ asymmetries between $D\to K^+K^-$ and $D\to \pi^+\pi^-$ has raised a debate whether the observed asymmetries can be regarded as a signal of physics beyond the standard model (SM). In this paper we obtain all the topological amplitudes and isospin amplitudes directly from measured observables for $D\to \pi\pi$. These results unambiguously imply a very large penguin contribution, having a central value $4.74$ times the magnitude of the amplitude for $D^0\to\pi^+ \pi^-$. This fitted central value differs from a reasonable SM estimate of $10\%$ with a significance greater than $3.3\sigma$. In contrast to previous studies, we present model-independent arguments based only on unitarity of re-scattering amplitudes to show that large penguins cannot arise from re-scattering alone and likely indicate physics beyond the SM. In a model-independent approach we show how a very small contribution from physics beyond the SM with a large weak phase alleviates the problem.

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 / 2 minor

Summary. The manuscript extracts topological and isospin amplitudes for D→ππ decays directly from measured observables, yielding a penguin amplitude whose magnitude is 4.74 times that of the D⁰→π⁺π⁻ amplitude. This central value is reported to differ from a reasonable SM estimate of ~10% by more than 3.3σ. The authors advance model-independent unitarity arguments based on rescattering amplitudes to conclude that such large penguins cannot arise from final-state interactions alone and therefore point to physics beyond the SM; they further illustrate how a small BSM contribution carrying a large weak phase can resolve the tension.

Significance. If the amplitude extraction is robust and the unitarity bound withstands scrutiny, the result would be significant for charm CP-violation studies, strengthening the case for BSM effects in a sector where SM predictions are under active debate. The direct, data-driven determination of amplitudes without additional model assumptions is a clear strength, as is the attempt to frame the rescattering argument in a model-independent way. The overall significance is reduced by dependence on an external SM benchmark whose uncertainty is not fully propagated and by the qualitative character of the unitarity constraint.

major comments (2)
  1. [Abstract] Abstract and the section presenting the numerical extraction: the stated >3.3σ tension with the SM estimate of 10% inherits the uncertainty of that external benchmark; without explicit propagation of the SM uncertainty into the significance, the tension claim cannot be evaluated at the quoted level.
  2. [Unitarity argument] The unitarity argument (the section following the amplitude fit): the claim that unitarity of the rescattering S-matrix forbids large effective penguins without BSM is presented as model-independent, yet it is secure only under the assumption of an effectively two-channel system or negligible inelastic couplings; a quantitative estimate of possible enhancement from coupled channels (KK, ηη, 4π, etc.) is required to support the necessity of BSM.
minor comments (2)
  1. [Amplitude definitions] Clarify the precise definition of the penguin-to-tree ratio used in the fit and ensure all amplitude normalizations are stated explicitly in the text and tables.
  2. [Discussion] Add a brief discussion of how the extracted amplitudes compare with existing global fits in the literature.

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 that will be incorporated in the updated version.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the section presenting the numerical extraction: the stated >3.3σ tension with the SM estimate of 10% inherits the uncertainty of that external benchmark; without explicit propagation of the SM uncertainty into the significance, the tension claim cannot be evaluated at the quoted level.

    Authors: We agree that the quoted significance relies on treating the SM benchmark of 10% as a fixed central value. In the revised manuscript we will explicitly state the range of SM estimates available in the literature, adopt a conservative uncertainty on this benchmark, and propagate it through the significance calculation. This will replace the current >3.3σ statement with a more precisely qualified tension level. revision: yes

  2. Referee: [Unitarity argument] The unitarity argument (the section following the amplitude fit): the claim that unitarity of the rescattering S-matrix forbids large effective penguins without BSM is presented as model-independent, yet it is secure only under the assumption of an effectively two-channel system or negligible inelastic couplings; a quantitative estimate of possible enhancement from coupled channels (KK, ηη, 4π, etc.) is required to support the necessity of BSM.

    Authors: The unitarity bound presented in the manuscript follows directly from the optical theorem and S-matrix unitarity applied to the two-body final states that dominate D→ππ decays. While we maintain that the argument is model-independent within the framework of two-body unitarity, we acknowledge that a quantitative bound on inelastic-channel enhancements would strengthen the presentation. In the revision we will add a short subsection that estimates the maximum possible contribution from coupled channels (KK, ηη, 4π) using multi-channel unitarity constraints and phase-space suppression factors, showing that even generous allowances fall short of the extracted penguin magnitude. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation from data and external benchmarks

full rationale

The paper extracts topological and isospin amplitudes directly from measured observables for D→ππ decays, yielding a fitted penguin magnitude of 4.74 times the D0→π+π− amplitude. This fitted value is compared to an external SM estimate of ~10% (producing the >3.3σ tension) and supported by unitarity arguments presented as model-independent within the paper. No quoted step reduces a claimed prediction or first-principles result to its own inputs by construction, nor relies on load-bearing self-citation or smuggled ansatz. The central results retain independent content from experimental inputs and external references, making the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the assumption that the measured observables can be expressed as linear combinations of topological amplitudes without additional unknown phases from final-state interactions beyond those already constrained by unitarity. The SM penguin size of 10% is taken as an external benchmark rather than derived inside the paper.

free parameters (1)
  • penguin-to-tree ratio
    Central value 4.74 obtained by solving the system of equations from measured branching fractions and CP asymmetries for D to pi pi.
axioms (1)
  • domain assumption Unitarity of rescattering amplitudes forbids large penguin contributions from final-state interactions alone
    Invoked to conclude that the observed size cannot arise within the SM.

pith-pipeline@v0.9.0 · 5743 in / 1379 out tokens · 26452 ms · 2026-05-19T13:29:23.470341+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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  1. $CP$ violation in singly Cabibbo suppressed $D\to \pi a_0(980)$ decays

    hep-ph 2026-04 unverdicted novelty 5.0

    Long-distance rescattering generates O(10^{-3}) direct CP asymmetries in D→πa0(980) decays.

  2. CP asymmetries in charged meson decay to two pions

    hep-ph 2026-05 unverdicted novelty 4.0

    CP asymmetries for B+ to pi+ pi0, D+ to pi+ pi0, and K+ to pi+ pi0 are estimated in the Standard Model at roughly 3 times 10 to the -3, 10 to the -5, and 10 to the -6 using a unified formalism for isospin violation.

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