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We carry out an analysis of the multibody decay cascade $\Lambda_b\to\Lambda^*_J J/\psi \to pK^- J/\psi$ with the $ \Lambda^*_J$ resonance including$\Lambda^*_{1520},\Lambda^*_{1600}$, and $\Lambda^*_{1800}$, and $J/\psi$reconstructed by the lepton pair final state. Using the helicity amplitudetechnique, we derive a compact form for the angular distributions for the decaychain, from which one can extract various one-dimensional distributions. Usingthe $\Lambda_b\to \Lambda_J^*$ form factors from lattice QCD and quark model,we calculate the differential and integrated partial widths. Decay branchingfractions are found as $\mathcal{B}(\Lambda_b\to \Lambda^*_J(pK)J/\psi(\ell^+\ell^-))=(1.35\pm0.28)\times 10^{-5}$. In addition, we alsoexplore forward-backward asymmetry, and various polarizations. Results in thiswork will serve a calibration for the study of $b\to s \ell^+\ell^-$ decays in$\Lambda_b$ decays in future and provide useful information towards theunderstanding of the properties of the $\Lambda_J^*$ baryons.

Angular distributions for $\Lambda_b\to \Lambda^*_J (pK^-)J/\psi$ Decays