The Emergence of the $\Delta U=0$ Rule in Charm Physics

Understand

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.