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

We calculate the invariant and helicity amplitudes for the transitions ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^{(*)}(J^P)+J/\psi$, where the ${\mathrm{\Lambda }}^{(*)}(J^P)$ are $\mathrm{\Lambda }(sud)$-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 ${\mathrm{\Lambda }}^{*}(1520,{\frac{3}{2}}^{-})$ and the ${\mathrm{\Lambda }}^{*}(1890,{\frac{3}{2}}^{+})$ are suppressed compared with those for the ground state $\mathrm{\Lambda }(1116,{\frac{1}{2}}^{+})$ and the excited state ${\mathrm{\Lambda }}^{*}(1405,{\frac{1}{2}}^{-})$. 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 ${\mathrm{\Lambda }}_b^0\to P_c^{+}(\to pJ/\psi )+K^{-}$ because the cascade decay chain ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^{*}({\frac{3}{2}}^{\pm })(\to p{K}^{-})+J/\psi$ involves the same final state.

Figure 1

The invariant mass $M(Kp)$ (left) and $M(J/\psi p)$ (right) distributions. Full LHCb model pseudodata are shown as black dots with error bars, while the hatched area corresponds to the $P_c^{+}$ exotic states. The main contributions from the ${\mathrm{\Lambda }}^{(*)}$ resonances are also shown.

Figure 2

Helicity angles ${\theta }_{{\mathrm{\Lambda }}^{\star }}$ (left) and ${\theta }_{J/\psi }$ (right) distributions for the low mass $M_{Kp}$ region ($M_{Kp}<1.55\mathrm{GeV}$). Full LHCb model (pseudodata) is shown as black dots with error bars, while the dotted line represent our calculation for the single $\mathrm{\Lambda }(1520)$ state. Solid red and blue lines correspond to our attempt to describe the pseudodata by taking into account only the 3 lowest ${\mathrm{\Lambda }}^{\star }$ states, see details in text.