Direct $CP$ violation of three bodies decay process from the resonance effect

TL;DR

This paper investigates direct CP violation in three-body meson decays caused by resonance effects and isospin symmetry breaking, predicting significant asymmetries near resonance regions and discussing experimental detection prospects.

Contribution

It introduces a new mechanism for CP violation arising from resonance interference and isospin breaking in three-body decays, with quantitative predictions for B meson decays.

Findings

CP asymmetry can be greatly enhanced near resonance regions

Resonance interference contributes to strong phases affecting CP violation

Potential for observing predicted CP violation at the LHC

Abstract

The physical state of $\rho$-$\omega$-$\phi$ mesons can be mixed by the unitary matrix. The decay processes of $\omega \rightarrow \pi^{+}\pi^{-}$ and $\phi \rightarrow \pi^{+}\pi^{-}$ are from the isospin symmetry breaking. The $\rho-\omega$, $\rho-\phi$ and $\omega-\phi$ interferences lead to resonance contribution to produce the strong phases. The $CP$ asymmetry is considered from above isospin symmetry breaking due to the new strong phase for the first order. It has been found the $CP$ asymmetry can be enhanced greatly for the decay process of $B^{0}\rightarrow\pi^+\pi^{-}\eta^{(')}$ when the invariant masses of the $\pi^+\pi^{-}$ pairs are in the area around the $\omega$ resonance range and the $\phi$ resonance range in perturbative QCD. We also discuss the possibility to search the predicted $CP$ violation at the LHC.