Paper detail

The Emergence of the $ΔU=0$ Rule in Charm Physics

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 $ΔU=0$ over $ΔU=1$ 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 $ΔI=1/2$ over $ΔI=3/2$ matrix elements in kaon decays, that is, the $ΔI=1/2$ rule. As a guideline for future measurements, we show how to completely solve the most general parametrization of the $D \to P^+P^-$ system.