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The Emergence of the $\Delta U=0$ Rule in Charm Physics
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abstract
We discuss the implications of the recent discovery of CP violation in two-body SCS $D$ decays by LHCb. We show that the result can be explained within the SM without the need for any large $SU(3)$ breaking effects. It further enables the determination of the imaginary part of the ratio of the $\Delta U=0$ over $\Delta U=1$ matrix elements in charm decays, which we find to be $(0.65\pm 0.12)$. Within the standard model, the result proves the non-perturbative nature of the penguin contraction of tree operators in charm decays, similar to the known non-perturbative enhancement of $\Delta I=1/2$ over $\Delta I=3/2$ matrix elements in kaon decays, that is, the $\Delta I=1/2$ rule. As a guideline for future measurements, we show how to completely solve the most general parametrization of the $D \to P^+P^-$ system.
Forward citations
Cited by 2 Pith papers
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$D\to P \ell^+\ell^-$ decays assisted by QCD light-cone sum rules
A new LCSR-assisted dispersion method predicts the D+ to pi+ l+ l- branching fraction and shows that the short-distance c to u l+ l- transition is practically invisible in the Standard Model.
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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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