Charmless 3-body B Decays: Resonant and Nonresonant Contributions

Abstract

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. $ $. This explains the dominance of the nonresonant background in $B\to KKK$ decays, the sizable nonresonant fraction of order $(35\sim 40)%$ in $K^-π^+π^-$ and $\bar K^0π^+π^-$ modes and the smallness of nonresonant rates in $B\to πππ$ 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 $\sin2β_{\rm eff}$ and $A_{CP}$ in $K^+K^-K_S,K_SK_SK_S,K_Sπ^+π^-$ and $K_Sπ^0π^0$ modes are estimated.