Two Body Hadronic Decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2}^{+})+P$ in a quark model

Abstract

The framework under which decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B(\frac{1}{2}^{+})+M$ are analyzed is not applicable for the decays $\Lambda_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2} ^{+})+M$. These decays occur through a baryon pole $\Sigma^{0}_{c}$ which is generated by the W-exchange diagram in the process $b+u \xrightarrow {W} c+d$. The effective Hamiltonian which arises from the W-exchange diagram is expressed in the non relativistic limit. Since $% \Sigma^{0}_{c}$ belongs to representation $6$ of SU(3), it contributes to two sets of decays: $\Lambda_{b}\rightarrow\Delta^{0}D^{0},\Delta^{-}D^{+},% \Sigma^{*-}D_s^{+}$ and $\Lambda_{b}\rightarrow\Sigma^{\ast-}_{c}\pi^{+},% \Sigma^{\ast 0}_{c}\pi^{0}\;, \Xi^{\ast 0}_{c}K^{0}$. The branching ratios for these decays are evaluated which can be compared with their experimental values when the data become available. Other prediction of the model is that asymmetry parameter $\alpha = 0$, since baryon pole contributes to parity conserving (p-wave) amplitude and does not contribute to parity violating (d-wave) amplitude.