Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to π^+π^-$ decays

[2505.24338] Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to π^+π^-$ decays Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Phenomenology arXiv:2505.24338 (hep-ph) [Submitted on 30 May 2025 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to π^+π^-$ decays Authors: Rahul Sinha , Thomas E. Browder , N. G. Deshpande , Dibyakrupa Sahoo , Nita Sinha View a PDF of the paper titled Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to \pi^+\pi^-$ decays, by Rahul Sinha and 3 other authors View PDF HTML (experimental) 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. Comments: 8 pages, 10 figures; Version to be published in Phys. Rev. D Subjects: High Energy Physics - Phenomenology (hep-ph) ; High Energy Physics - Experiment (hep-ex) Cite as: arXiv:2505.24338 [hep-ph] (or arXiv:2505.24338v3 [hep-ph] for this version) https://doi.org/10.48550/arXiv.2505.24338 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. D 113, 093003 (2026) Related DOI : https://doi.org/10.1103/lppq-czdd Focus to learn more DOI(s) linking to related resources Submission history From: Rahul Sinha [ view email ] [v1] Fri, 30 May 2025 08:28:36 UTC (6,121 KB) [v2] Thu, 12 Jun 2025 08:08:39 UTC (6,121 KB) [v3] Thu, 9 Apr 2026 06:53:17 UTC (6,122 KB) Full-text links: Access Paper: View a PDF of the paper titled Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to \pi^+\pi^-$ decays, by Rahul Sinha and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-ph < prev | next > new | recent | 2025-05 Change to browse by: hep-ex References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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