Patterns of CP violation from mirror symmetry breaking in the η→π+π−π0 Dalitz plot

Susan Gardner,Jun Shi

doi:10.1103/physrevd.101.115038

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 $I=0$.

Highlights

The decay η → 3π first came to prominence after the observation of KL → πþπ− decay and the discovery of CP violation in 1964 [1], because it could be used to test whether KL → πþπ− decay was generated by CP violation in the weak interactions [2,3]
CP violation could arise from the interference of the CP-conserving weak interaction with a new, “strong” interaction that breaks C and CP; this new interaction could be identified through the appearance of a charge asymmetry in the momentum distribution of πþ and π− in η → πþπ−π0 decay [2,4,5]
Since the C transformation on the decay amplitude is equivalent to t ↔ u exchange [42], we see that the appearance of terms that are odd in X would indicate both C and CP violation

Summary

INTRODUCTION

The decay η → 3π first came to prominence after the observation of KL → πþπ− decay and the discovery of CP violation in 1964 [1], because it could be used to test whether KL → πþπ− decay was generated by CP violation in the weak interactions [2,3]. CP violation could arise from the interference of the CP-conserving weak interaction with a new, “strong” interaction that breaks C and CP; this new interaction could be identified through the appearance of a charge asymmetry in the momentum distribution of πþ and π− in η → πþπ−π0 decay [2,4,5]. A charge asymmetry could arise from the interference of a C-conserving, but isospin-breaking amplitude with a isospin-conserving, but C-violating one [4]. We believe that the study of the Dalitz plot distribution in η → πþðpπþ Þπ−ðpπ− Þπ0ðpπ0 Þ decay is an ideal arena in which to search for C and CP violation beyond the SM. EDM could be mediated by a minimal P- and T-violating interaction, the mass-dimension-four θterm of the SM, and not new weak-scale physics. The appearance of a charge asymmetry and of C (and CP) violation in η → πþðpπþ Þπ−ðpπ− Þπ0ðpπ0 Þ decay can be probed experimentally through the measurement of a left-right asymmetry, ALR [28]: ALR

Ntot ðNþ

THEORETICAL FRAMEWORK

RESULTS

SUMMARY

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