Charmless 3-body B Decays: Resonant and Nonresonant Contributions

Charmless 3-body decays of $B$ mesons are studied using a simple model based on the framework of the factorization approach. We have identified a large source of the nonresonant signal in the matrix elements of scalar densities, e.g. $<K\bar{K}\mathrm{\mid }\bar{s}s\mathrm{\mid }0>$. This explains the dominance of the nonresonant background in $B\to KKK$ decays, the sizable nonresonant fraction of order $(35\sim 40)$ in $K^{-}{\pi }^{+}{\pi }^{-}$ and ${\bar{K}}^0{\pi }^{+}{\pi }^{-}$ modes and the smallness of nonresonant rates in $B\to \pi \pi \pi$ decays. We have computed the resonant and nonresonant contributions to charmless 3-body decays and determined the rates for the quasi-two-body decays $B\to VP$ and $B\to SP$. Time-dependent CP asymmetries $\sin 2{\beta }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and $A_{CP}$ in $K^{+}{K}^{-}{K}_S,K_S{K}_S{K}_S,K_S{\pi }^{+}{\pi }^{-}$ and $K_S{\pi }^0{\pi }^0$ modes are estimated.