Determination of the D →ππ ratio of penguin over tree diagrams

Margarita Gavrilova, Yuval Grossman, Stefan Schacht

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We study the penguin over tree ratio in D→ππ decays. This ratio can serve as a probe for rescattering effects. Assuming the Standard Model and in the isospin limit, we derive expressions that relate both the magnitude and the phase of this ratio to direct CP asymmetries and branching fractions. We find that the current data suggest that rescattering is large. A dedicated experimental analysis with current and future data will be able to significantly reduce the errors on these determinations, and enable us to check if indeed there is significant rescattering in D→ππ decays.

Original languageEnglish
Article number033011
JournalPhysical Review D
Issue number3
StatePublished - 1 Feb 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 authors. Published by the American Physical Society.


We thank Marco Gersabeck and Ulrich Nierste for useful discussions. The work of M. G. was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and No. NSF PHY-2309135, the Heising-Simons Foundation, and the Simons Foundation (216179, LB). Y. G. is supported in part by the NSF Grant No. PHY-2014071. S. S. is supported by a Stephen Hawking Fellowship from UKRI under reference No. EP/T01623X/1 and the STFC research Grants No. ST/T001038/1 and No. ST/X00077X/1. This work uses existing data which is available at locations cited in the bibliography.

FundersFunder number
National Science FoundationPHY-2309135, PHY-1748958
Simons Foundation216179, PHY-2014071
UK Research and InnovationEP/T01623X/1
Heising-Simons Foundation
Science and Technology Facilities CouncilST/X00077X/1, ST/T001038/1


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