Evidence of $A_{CP}(D^0\to {\pi }^{+}{\pi }^{-})$ implies observable $CP$ violation in the $D^0\to {\pi }^0{\pi }^0$ decay

Abstract

Inspired by the recent measurement of $CP$ asymmetry in the individual mode on LHCb, we study $CP$ asymmetry of the $D\to \pi \pi$ system in the isospin and topological analysis. The ratio between penguin and tree amplitudes $P/(T+C)$ in the $D\to \pi \pi$ system is found to be greater than two in most values of the relative strong phase. And $D^0\to {\pi }^0{\pi }^0$ is a potential mode to reveal the $CP$ asymmetry of the order of $10^{-3}$, which would be observed by Belle II in the future. The large $CP$ asymmetry in the $D\to \pi \pi$ system might be understood in the $t$-channel final-state interaction.

arXiv comment11 pages, 7 figures, published version

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Cited by in corpus (5)

• Final-state interactions in the CP asymmetries of charm-meson two-body decays
• Two is better than one: The U-spin-CP anomaly in charm
• Isospin sum rules in charmed baryon weak decays
• Implications of recent LHCb data on CPV in b-baryon four body decays
• Measurement of the time-integrated $CP$ asymmetry in $D^0\to {\pi }^0{\pi }^0$ decays at Belle II