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

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