Analysis of localized CP asymmetry in $\bar{B}_{s}^{0} \rightarrow \pi ^+\pi ^-\pi^{0}(K^{0})$

TL;DR

This paper investigates localized CP asymmetries in ar;B_s^0 processes, considering interference effects of  ho^0, , and  mesons, revealing significant asymmetries influenced by isospin symmetry breaking.

Contribution

It introduces the consideration of three-particle meson interference effects in analyzing CP asymmetries in ar;B_s^0 decays, providing new insights into their differential asymmetry.

Findings

Differential CP asymmetry can reach about 65% for ar;B_s^0 decays.

Localized CP asymmetry is significant below the  ho(770)^0 mass.

Interference effects of  ho^0, , and  mesons are crucial for understanding CP violation.

Abstract

An investigation about localized CP asymmetries for the processes of $\bar{B}_{s}^{0} \rightarrow \pi^{+}\pi^{-}\pi^{0} (K^{0})$ is presented in this paper. The innovation of this paper is that there is a consideration of three-particle $\rho^0(770)$, $\omega(782)$ and $\phi(1020)$ interferences effect. Generally, $\omega(782)$ and $\phi(1020)$ both can decay into $\pi ^+\pi ^-$ pair where can cause extremely small contribution from isospin symmetry breaking. Nevertheless, our analysis shows that $\bar{B}_{s}^{0} \rightarrow \pi ^+\pi ^-\pi^{0}(K^{0})$ decay process can bring differential CP asymmetry about $65\%$ ($36\%$) because of isospin symmetry breaking. To better compared with the data from experimental in the future, we integrate CP asymmetry over the invariant mass and obtain localized CP asymmetry value for the decay $\bar{B}_{s}^{0} \rightarrow \pi ^+\pi ^-\pi^{0} (K^{0})$. We find that there is an evident signal about CP asymmetry at invariant mass value $m(\pi^{+}\pi^{-})$ below the mass of $\rho(770)^{0}$ with the decay $\bar{B}_{s}^{0} \rightarrow \pi ^+\pi^{-}\pi^{0}$.