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

## TL;DR

This paper explains recent CP violation observations in charm decays within the Standard Model, revealing a non-perturbative enhancement similar to the kaon $rac{1}{2}$ rule, and provides a framework for future decay measurements.

## Contribution

It demonstrates that the observed CP violation can be explained without large $SU(3)$ breaking and introduces a method to determine the ratio of $ riangle U=0$ to $ riangle U=1$ matrix elements in charm decays.

## Key findings

- The imaginary part of the ratio of matrix elements is $(0.65\u00b1 0.12)$.
- CP violation can be explained within the Standard Model without large $SU(3)$ breaking.
- The results indicate a non-perturbative nature of penguin contractions in charm decays.

## 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.