Analysis of localized CP asymmetry in

De-Sen Shi; Gang Lü; Yan-Lin Zhao; Na-Wang Na-Wang; Xin-Heng Guo

doi:10.1140/epjc/s10052-023-11478-y

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 327
https://doi.org/10.1140/epjc/s10052-023-11478-y

Regular Article - Theoretical Physics

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

De-Sen Shi¹, Gang Lü¹^b, Yan-Lin Zhao¹, Na-Wang¹ and Xin-Heng Guo²

¹ Institute of Theoretical Physics, School of Sciences, Henan University of Technology, 450001, Zhengzhou, China
² College of Nuclear Science and Technology, Beijing Normal University, 100875, Beijing, China

^b ganglv66@sina.com

Received: 22 December 2022
Accepted: 29 March 2023
Published online: 26 April 2023

Abstract

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

© The Author(s) 2023

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