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Charmless Three-body Decays of B_s Mesons

Branching fractions and CP-violating asymmetries of charmless $B_s\to PPP$ decays with $P=K,π$ are studied using a simple model based on the factorization approach. The penguin-dominated modes $B_s\to \bar K^0 K^+π^-$ and $K^0K^-π^+$ have the largest rates among the three-body $B_s$ decays and they are dominated by the $K_0^*(1430)$ resonances and nonresonant contributions. The branching fraction of $B_s\to K^0K^+K^-$ 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 $K^0π^+π^-$, $K^0π^0π^0$, $K^0K^+K^-$ and $K_SK_SK_S$ channels. Just as the $B_u$ sector, the correlation of CP asymmetries $A_{CP}(B_s\to K^0π^+π^-)\approx -A_{CP}(B_s\to K^0K^+K^-)$ 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, $<K^0K|\bar dq|0>$ and $<\bar K^0π|\bar sq|0>$, is badly broken, the derived $U$-spin relations are generally not well respected.