Angular distributions for ${\Lambda }_b\to {\Lambda }_J^{\ast }(p{K}^{-})J/\psi$ Decays

Abstract

We carry out an analysis of the multibody decay cascade ${\Lambda }_b\to {\Lambda }_J^{\ast }J/\psi \to p{K}^{-}J/\psi$ with the ${\Lambda }_J^{\ast }$ resonance including ${\Lambda }_{1520}^{\ast },{\Lambda }_{1600}^{\ast }$, and ${\Lambda }_{1800}^{\ast }$, and $J/\psi$ 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 ${\Lambda }_b\to {\Lambda }_J^{\ast }$ form factors from lattice QCD and quark model, we calculate the differential and integrated partial widths. Decay branching fractions are found as $\mathcal{B}({\Lambda }_b\to {\Lambda }_J^{\ast }(pK)J/\psi ({\ell }^{+}{\ell }^{-}))=(1.35\pm 0.28)\times 10^{-5}$. 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 ${\Lambda }_b$ decays in future and provide useful information towards the understanding of the properties of the ${\Lambda }_J^{\ast }$ baryons.

Comments: 17 pages, 7 figures