Angular distributions for $Λ_b\to Λ^*_J (pK^-)J/ψ$ Decays

Abstract

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