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

Abstract

The framework under which decays $Λ_{b}(\frac{1}{2}^{+})\rightarrow B(\frac{1}{2}^{+})+M$ are analyzed is not applicable for the decays $Λ_{b}(\frac{1}{2}^{+})\rightarrow B^{\ast}(\frac{3}{2} ^{+})+M$. These decays occur through a baryon pole $Σ^{0}_{c}$ 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 $% Σ^{0}_{c}$ belongs to representation $6$ of SU(3), it contributes to two sets of decays: $Λ_{b}\rightarrowΔ^{0}D^{0},Δ^{-}D^{+},% Σ^{*-}D_s^{+}$ and $Λ_{b}\rightarrowΣ^{\ast-}_{c}π^{+},% Σ^{\ast 0}_{c}π^{0}\;, Ξ^{\ast 0}_{c}K^{0}$. 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 $α= 0$, since baryon pole contributes to parity conserving (p-wave) amplitude and does not contribute to parity violating (d-wave) amplitude.