Exclusive charmless nonleptonic decays of the Bd0 meson in the standard model.

Abstract

We have studied the charmless nonleptonic decay such as the ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$, ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{*+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays, which include contributions from both Born process and penguin process, in the standard model. The branching ratios of these three decays are predicted to be \ensuremath{\sim}${10}^{\ensuremath{-}5}$, \ensuremath{\sim}${10}^{\ensuremath{-}5}$-${10}^{\ensuremath{-}6}$, and \ensuremath{\sim}${10}^{\ensuremath{-}5}$, respectively. For the ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay, the amplitude is dominated by the timelike penguin process. For the ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ decay, the dominant amplitude follows from the spacelike penguin process, which is ambiguous due to the annihilation form factor. For the ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{*+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay, the contributions of the three processes are comparable to each other. The precise determination of the annihilation form factor is necessary to predict reliably the branching ratios of the ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${B}_{d}^{0}\ensuremath{\rightarrow}{K}^{*+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays.