Polarization observables in semileptonic $V\to P$ decays of quarkonia

Abstract

We investigate the weak semileptonic decays of the charmonium $J/\psi$ and bottomonium $\Upsilon(1S)$ into a pseudoscalar meson, namely, the $J/\psi\to D_{(s)}\ell\bar{\nu}_\ell$ and $\Upsilon(1S)\to B_{(c)}\ell\bar{\nu}_\ell$ decays. We focus on the polarization observables including the forward-backward asymmetry, final lepton polarization, and lepton-side convexity parameter. In order to define these quantities, we apply the helicity amplitude method and obtain a twofold angular decay distribution for a general $V\to P\ell\bar{\nu}_\ell$ case. The hadronic form factors are taken from our previous work, where they were calculated in the Covariant Confined Quark Model. We provide theoretical predictions for the polarization observables and compare them with the literature.