Updated measurement of $CP$ violation and polarisation in $B_s^0\to J\mathrm{/}\psi \bar{K}{}^{\ast }(892{)}^0$ decays

A time-integrated angular analysis of the decay $B_s^0\to J\mathrm{/}\psi \bar{K}{}^{\ast }(892{)}^0$, with $J\mathrm{/}\psi \to {\mu }^{+}{\mu }^{-}$ and $\bar{K}{}^{\ast }(892{)}^0\to K^{-}{\pi }^{+}$, is presented. The analysis employs a sample of proton-proton collision data collected by the LHCb experiment during 2015-2018 at a centre-of-mass energy of $13\text{TeV}$, corresponding to an integrated luminosity of $6{\text{fb}}^{-1}$. A simultaneous maximum-likelihood fit is performed to the angular distributions in bins of the $K^{-}{\pi }^{+}$ mass. This fit yields measurements of the $CP$-averaged polarisation fractions and $CP$ asymmetries for the P-wave component of the $K^{-}{\pi }^{+}$ system. The longitudinal and parallel polarisation fractions are determined to be $f_0=0.534\pm 0.012\pm 0.009$ and $f_{\parallel }=0.211\pm 0.014\pm 0.005$, respectively, where the first uncertainty is statistical and the second is systematic. The $CP$ asymmetries are measured with $3$-$7\mathrm{\%}$ precision and are found to be consistent with zero. These measurements, along with an updated determination of the branching fraction relative to the $B^0\to J\mathrm{/}\psi K^{\ast 0}$ decay, are combined with previous LHCb results, providing the most precise values for these observables to date.