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

Abstract

The first observation of ${\bar{B}}_d^0\to D^0{\bar{K}}^0$ and ${\bar{B}}_d^0\to D^0{\bar{K}}^{\ast 0}$ transitions by the Belle Collaboration allows us to do a complete isospin analysis of $B\to D{K}^{(\ast )}$ decay modes. We find that their respective isospin phase shifts are very likely to lie in the ranges $37^{\circ }\le ({\varphi }_1-{\varphi }_0{)}_{DK}\le 63^{\circ }$ (or around $50^{\circ }$) and $25^{\circ }\le ({\varphi }_1-{\varphi }_0{)}_{D{K}^{\ast }}\le 50^{\circ }$ (or around $35^{\circ }$), although the possibility $({\varphi }_1-{\varphi }_0{)}_{DK}=({\varphi }_1-{\varphi }_0{)}_{D{K}^{\ast }}=0^{\circ }$ cannot be ruled out at present. Thus significant final-state rescattering effects are possible to exist in such exclusive $|\Delta B|=|\Delta C|=|\Delta S|=1$ processes. We determine the spectator and color-suppressed spectator quark-diagram amplitudes of $B\to DK$ and $B\to D{K}^{\ast }$ decays, and compare them with the corresponding quark-diagram amplitudes of $B\to D\pi$ and $B\to D\rho$ 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 ${\bar{B}}_d^0\to {\bar{D}}^0{\bar{K}}^{(\ast )0}$, $B_u^{-}\to {\bar{D}}^0{K}^{(\ast )-}$ and $B_u^{-}\to D^{-}{\bar{K}}^{(\ast )0}$ transitions.

Comments: LaTex 14 pages (3 PS figures included). More delicate numerical results are presented. Version accepted for publication in Eur. Phys. J. C