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CP-violating asymmetries in B^0 decays to K^+K^-K_{S(L)}^0 and K_S^0K_S^0K_{S(L)}^0

Decay rates and time-dependent and direct CP asymmetries in the decays $B^0\to K^+K^-K_{S(L)}$ and $K_S K_S K_{S(L)}$ are studied. Resonant and nonresonant contributions to the three-body decays are carefully investigated. Nonresonant effects on 2-body and 3-body matrix elements are constrained by QCD counting rules. The predicted branching ratios are consistent with the data within the theoretical and experimental errors, though the theoretical central values are somewhat smaller than the experimental ones. Owing to the presence of color-allowed tree amplitudes in $B^0\to K^+K^-K_{S(L)}$, this penguin-dominated mode is subject to a significant tree pollution and the deviation of the mixing-induced \CP asymmetry from that measured in $B\to J/ψK_S$, namely, $Δ\sin 2β_{K^+K^-K_{S(L)}}\equiv \sin 2β_{K^+K^-K_{S(L)}}-\sin 2 β_{J/ψK_S}$, can be as large as O(0.10). In contrast, the $K_SK_SK_{S(L)}$ modes appear theoretically very clean in our picture with negligible $Δ\sin 2β_{K_SK_SK_{S(L)}}$. Direct CP asymmetries in $K^+K^-K_{S(L)}$ and $K_S K_S K_{S(L)}$ modes are found to be very small.