# Patterns of CP violation from mirror symmetry breaking in the $\eta\to\pi^+\pi^-\pi^0$ Dalitz plot

## TL;DR

This paper investigates mirror symmetry violation in the eta decay Dalitz plot, revealing that CP-violating amplitudes with isospin 2 are more suppressed than those with isospin 0, providing insights into underlying symmetry breaking.

## Contribution

It introduces a method to reconstruct the isospin of CP-violating structures from Dalitz plot data and applies it to recent experiments, uncovering new suppression patterns.

## Key findings

- CP-violating amplitude with isospin I=2 is highly suppressed.
- Analysis of experimental data confirms isospin dependence of CP violation.
- Provides a new approach to study symmetry breaking in meson decays.

## Abstract

A violation of mirror symmetry in the $\eta\to\pi^+\pi^-\pi^0$ Dalitz plot has long been recognized as a signal of C and CP violation. Here we show how the isospin of the underlying C- and CP-violating structures can be reconstructed from their kinematic representation in the Dalitz plot. Our analysis of the most recent experimental data reveals, for the first time, that the C- and CP-violating amplitude with total isospin $I=2$ is much more severely suppressed than that with total isospin $I=0$.