The resonances $X(4140)$, $X(4160)$, and $P_{cs}(4459)$ in the decay of $\Lambda_b\to J/\psi\Lambda\phi$

We study the decay of $\Lambda_b\to J/\psi\Lambda\phi$ by taking into account the intermediate resonances $X(4140)$, $X(4160)$, and $P_{cs}(4459)$. In addition to the peak of the $X(4140)$, we also find a bump structure around 4160 MeV followed by a cusp structure around $D^*_s\bar{D}^*_s$ threshold in the $J/\psi\phi$ invariant mass distribution of the $\Lambda_b\to J/\psi\Lambda\phi$ process, which can be associated to the $D^*_s\bar{D}^*_s$ molecular state $X(4160)$. We also show that this reaction can also be used to confirm the existence of the hidden-charm pentaquark $P_{cs}(4459)$ with strangeness. We predict an enhancement structure close to the threshold in the $D^*_s\bar{D}^*_s$ invariant mass distribution of the $\Lambda_b\to D^*_s\bar{D}^*_s\Lambda$ process, which is the reflection of the $X(4160)$ and should not be misidentified with a new resonance. We strongly suggest experimentalists to further measure these processes, which can be useful to clarify the nature of $X(4140)$ and $X(4160)$ resonances, and to confirm the existence of the $P_{cs}(4459)$.
Comment: 8 pages, 10 figures