Resonances X (4140 ), X (4160 ) , and P c s (4459 ) in the decay of Λ b →J /ψ Λ ϕ

We study the decay of ${\\mathrm{\\ensuremath{\\Lambda}}}_{b}\\ensuremath{\\rightarrow}J/\\ensuremath{\\psi}\\mathrm{\\ensuremath{\\Lambda}}\\ensuremath{\\phi}$ 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 ${D}_{s}^{*}{\\overline{D}}_{s}^{*}$ threshold in the $J/\\ensuremath{\\psi}\\ensuremath{\\phi}$ invariant mass distribution of the ${\\mathrm{\\ensuremath{\\Lambda}}}_{b}\\ensuremath{\\rightarrow}J/\\ensuremath{\\psi}\\mathrm{\\ensuremath{\\Lambda}}\\ensuremath{\\phi}$ process, which can be associated to the ${D}_{s}^{*}{\\overline{D}}_{s}^{*}$ 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 ${D}_{s}^{*}{\\overline{D}}_{s}^{*}$ invariant mass distribution of the ${\\mathrm{\\ensuremath{\\Lambda}}}_{b}\\ensuremath{\\rightarrow}{D}_{s}^{*}{\\overline{D}}_{s}^{*}\\mathrm{\\ensuremath{\\Lambda}}$ 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 ${P}_{cs}(4459)$.