Two Body Hadronic Decays ${\Lambda }_b({\frac{1}{2}}^{+})\to B^{\ast }({\frac{3}{2}}^{+})+P$ in a quark model

Abstract

The framework under which decays ${\Lambda }_b({\frac{1}{2}}^{+})\to B({\frac{1}{2}}^{+})+M$ are analyzed is not applicable for the decays ${\Lambda }_b({\frac{1}{2}}^{+})\to B^{\ast }({\frac{3}{2}}^{+})+M$. These decays occur through a baryon pole ${\Sigma }_c^0$ which is generated by the W-exchange diagram in the process $b+u\stackrel{W}{\to }c+d$. The effective Hamiltonian which arises from the W-exchange diagram is expressed in the non relativistic limit. Since belongs to representation $6$ of SU(3), it contributes to two sets of decays: ${\Lambda }_b\to {\Delta }^0{D}^0,{\Delta }^{-}{D}^{+},$ and ${\Lambda }_b\to {\Sigma }_c^{\ast -}{\pi }^{+},$. 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.

Comments: No Figure, 10 pages, A version that appeared in the Physics Review D