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Determination of the $D\rightarrow \pi\pi$ ratio of penguin over tree diagrams
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abstract
We study the penguin over tree ratio in $D\rightarrow \pi\pi$ 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 $D \to \pi \pi$ decays.
Forward citations
Cited by 3 Pith papers
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Search for $CP$ violation in $\Xi_c^+\to\Sigma^+h^+h^-$ and $\Lambda_c^+\to ph^+h^-$ at Belle II
First individual A_CP measurements for Xi_c+ -> Sigma+ h+h- and Lambda_c+ -> p h+h- decays, all consistent with CP symmetry and with U-spin sum-rule predictions.
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Measurement of the CP asymmetry in $D^+ \to \pi^+ \pi^0$ decays at Belle II
The new world-best measurement of the CP asymmetry in D+ -> pi+ pi0 decays is (-1.8 +/- 0.9 +/- 0.1)%, consistent with zero and with the Standard Model.
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Measurement of the time-integrated $CP$ asymmetry in $D^0\to\pi^0\pi^0$ decays at Belle II
Belle II measures A_CP(D0 -> pi0 pi0) = (0.30 ± 0.72 ± 0.20)%, consistent with no CP violation and with the previous Belle measurement.
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