Updated measurement of $CP$ violation and polarisation in $B^0_s \rightarrow J/ψ\overline{K}{}^{*}\kern-1pt(892)^{0}$ decays

Abstract: A time-integrated angular analysis of the decay $B^0_s \rightarrow J/\psi \overline{K}{}^{*}\kern-1pt(892)^{0}$, with $J/\psi \rightarrow \mu^{+} \mu^{-}$ and $\overline{K}{}^{*}\kern-1pt(892)^{0} \rightarrow K^{-} \pi^{+}$, 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 $3$-$7\%$ precision and are found to be consistent with zero. These measurements, along with an updated determination of the branching fraction relative to the $B^0 \rightarrow J/\psi K^{*0}$ decay, are combined with previous LHCb results, providing the most precise values for these observables to date.