Final-state Rescattering and SU(3) Symmetry Breaking in B->DK and B->DK^* Decays

Abstract

The first observation of $\bar{B}^0_d\to D^0\bar{K}^0$ and $\bar{B}^0_d\to D^0\bar{K}^{*0}$ transitions by the Belle Collaboration allows us to do a complete isospin analysis of $B\to DK^{(*)}$ decay modes. We find that their respective isospin phase shifts are very likely to lie in the ranges $37^\circ \leq (ϕ_1 -ϕ_0)_{DK} \leq 63^\circ$ (or around $50^\circ$) and $25^\circ \leq (ϕ_1 -ϕ_0)_{DK^*} \leq 50^\circ$ (or around $35^\circ$), although the possibility $(ϕ_1 -ϕ_0)_{DK} = (ϕ_1 -ϕ_0)_{DK^*} = 0^\circ$ cannot be ruled out at present. Thus significant final-state rescattering effects are possible to exist in such exclusive $|ΔB| = |ΔC| = |ΔS| =1$ processes. We determine the spectator and color-suppressed spectator quark-diagram amplitudes of $B\to DK$ and $B\to DK^*$ decays, and compare them with the corresponding quark-diagram amplitudes of $B\to Dπ$ and $B\to Dρ$ decays. The effects of SU(3) flavor symmetry breaking are in most cases understandable in the factorization approximation, which works for the individual isospin amplitudes. Very instructive predictions are also obtained for the branching fractions of rare $\bar{B}^0_d \to \bar{D}^0 \bar{K}^{(*)0}$, $B^-_u \to \bar{D}^0 K^{(*)-}$ and $B^-_u \to D^- \bar{K}^{(*)0}$ transitions.