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

Abstract

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 $B\to J/\psi K_S$, namely, $\Delta \sin 2{\beta }_{K^{+}{K}^{-}{K}_{S(L)}}\equiv \sin 2{\beta }_{K^{+}{K}^{-}{K}_{S(L)}}-\sin 2{\beta }_{J/\psi K_S}$, can be as large as O(0.10). In contrast, the $K_S{K}_S{K}_{S(L)}$ modes appear theoretically very clean in our picture with negligible $\Delta \sin 2{\beta }_{K_S{K}_S{K}_{S(L)}}$. Direct CP asymmetries in $K^{+}{K}^{-}{K}_{S(L)}$ and $K_S{K}_S{K}_{S(L)}$ modes are found to be very small.

Comments: 17 pages and 2 figures, the tree contribution is modified due to the new data from BaBar, to appear in Phys. Rev. D