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}) 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 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} 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 ^{0}(770) with the decay {bar{B}}_{s}^{0} rightarrow pi ^+pi ^{-}pi ^{0}.