Charmless Three-body Decays of B_s Mesons

Abstract

Branching fractions and CP-violating asymmetries of charmless $B_s\to PPP$ decays with $P=K,\pi$ are studied using a simple model based on the factorization approach. The penguin-dominated modes $B_s\to {\bar{K}}^0{K}^{+}{\pi }^{-}$ and $K^0{K}^{-}{\pi }^{+}$ have the largest rates among the three-body $B_s$ decays and they are dominated by the $K_0^{\ast }(1430)$ resonances and nonresonant contributions. The branching fraction of $B_s\to K^0{K}^{+}{K}^{-}$ is predicted to be $1.4\times 10^{-6}$, which is close to the high end of the measured result $(0.2-3.4)\times 10^{-6}$ obtained by LHCb. We find sizable CP violation in $K^0{\pi }^{+}{\pi }^{-}$, $K^0{\pi }^0{\pi }^0$, $K^0{K}^{+}{K}^{-}$ and $K_S{K}_S{K}_S$ channels. Just as the $B_u$ sector, the correlation of CP asymmetries $A_{CP}(B_s\to K^0{\pi }^{+}{\pi }^{-})\approx -A_{CP}(B_s\to K^0{K}^{+}{K}^{-})$ holds in $B_s$ decays. Several model-independent relations based on $U$-spin symmetry for CP asymmetries are derived. Although they cannot be tested by the present available data, they can be checked by the dynamical calculations. Since the $U$-spin symmetry which relates various matrix elements of scalar densities, for example, $<K^{0}K|\bar{d}q|0>$ and $<{\bar{K}}^0\pi |\bar{s}q|0>$, is badly broken, the derived $U$-spin relations are generally not well respected.

Comments: 15 pages, two figures; Tables I-III and Figs. 1-2 are updated; a new U-spin symmetry relation is added to Eq. (3.6); PRD version