Theoretical description of the decays ${\Lambda }_b\to {\Lambda }^{(\ast )}({\frac{1}{2}}^{\pm },{\frac{3}{2}}^{\pm })+J/\psi$

Abstract

We calculate the invariant and helicity amplitudes for the transitions ${\Lambda }_b\to {\Lambda }^{(\ast )}(J^P)+J/\psi$ where the ${\Lambda }^{(\ast )}(J^P)$ are $\Lambda (sud)$-type ground and excited states with $J^P$ quantum numbers $J^P={\frac{1}{2}}^{\pm },{\frac{3}{2}}^{\pm }$. The calculations are performed in the framework of a covariant confined quark model previously developed by us. We find that the values of the helicity amplitudes for the ${\Lambda }^{\ast }(1520,{\frac{3}{2}}^{-})$ and the ${\Lambda }^{\ast }(1890,{\frac{3}{2}}^{+})$ are suppressed compared with those for the ground state $\Lambda (1116,{\frac{1}{2}}^{+})$ and the excited state ${\Lambda }^{\ast }(1405,{\frac{1}{2}}^{-})$. This analysis is important for the identification of the hidden charm pentaquark states $P_c^{+}(4380)$ and $P_c^{+}(4450)$ which were discovered in the decay chain ${\Lambda }_b^0\to P_c^{+}(\to pJ/\psi )+K^{-}$ because the cascade decay chain ${\Lambda }_b\to {\Lambda }^{\ast }({\frac{3}{2}}^{\pm })(\to p{K}^{-})+J/\psi$ involves the same final state.

Comments: 15 pages, 4 figures. Minor corrections done