The first measurement of ${C P}$ asymmetries in the decay ${B_s^0\to J/\psi \overline{K}^{*}(892)^{0}}$ and an updated measurement of its branching fraction and polarisation fractions are presented. The results are obtained using data corresponding to an integrated luminosity of $3.0 fb^{1}$ of protonproton collisions recorded with the LHCb detector at centreofmass energies of $7$ and $8 \mathrm{TeV}$. Together with constraints from ${B^0\to J/\psi \rho^0}$, the results are used to constrain additional contributions due to penguin diagrams in the ${C P}$violating phase ${{\phi}_{s}}$, measured through ${B_s^0}$ decays to charmonium.
Decay topologies contributing to the $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \phi$ channel (a,b) and $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \overline{ K}{} ^{*0} $ channel (c,d). The tree diagrams (a,c) are shown on the left and the penguin diagrams (b,d) on the right. 
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The $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^ \pi^+ $ invariant mass distribution with the sum of the fit projections in the 20 $ m_{ K^ \pi^+ }$ and $\cos(\theta_{\mu})$ bins. Points with error bars show the data. The projection of the fit result is represented by the solid blue line, and the contributions from the different components are detailed in the legend. At this scale the contribution of the $\Lambda^0_b \to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} p \pi^$ is barely visible. All the other peaking background components are subtracted as described in the text. 
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Representation of helicity angles as discussed in the text. 
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Efficiency corrected $ m_{ K^ \pi^+ }$ distribution for $ B^0_s$ shown in squares (red) and $\overline{ B}{} ^0$ shown in circles (black) using $sW eights$ computed from the maximum likelihood fit to the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^ \pi^+ $ invariant mass spectrum. 
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Fitted signal distributions compared with the weighted angular distributions with $ B^0_s$ $sW eights$ . Points with error bars show the data. The projection of the fit result is represented by the solid black line, and the contributions from the different amplitude components are described in the legend. 
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Limits on the penguin parameters $a_i$ and $\theta_i$ obtained from intersecting contours derived from the $ {C P}$ asymmetries and branching fraction information in $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \overline{ K}{} ^{*0} $. Superimposed are the confidence level contours obtained from a $\chi^2$ fit to the data. Shown are the longitudinal (top), parallel (middle) and perpendicular (bottom) polarisation. 
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Dependence of the uncertainty on the penguin shift $\Delta\phi_{s,i}^{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \phi}$ on the uncertainty on $\xi$. The bands correspond to the 68% C.L. The longitudinal (top), parallel (middle) and perpendicular (bottom) polarisations are shown. 
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Limits on the penguin parameters $a_i$ and $\theta_i$ obtained from intersecting contours derived from the $ {C P}$ asymmetries and branching fraction information in $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \overline{ K}{} ^{*0} $ and $ B^0 \to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \rho^0$. Superimposed are the confidence level contours obtained from a $\chi^2$ fit to the data. The longitudinal (top), parallel (middle) and perpendicular (bottom) polarisations are shown. 
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Animated gif made out of all figures. 
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Expected yields of each background component in the signal mass range. 
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The $C_{\rm SP}$, $C_{\rm SD}$ and $C_{\rm PD}$ factors calculated in each of the four $ m_{ K^ \pi^+ }$ bins around the $\overline{ K}{} ^{*0}$ peak. 
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Summary of the measured $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \overline{ K}{} ^{*0} $ {\rm Pwave} properties and their statistical and systematic uncertainties. When no value is given, it means an uncertainty below $5\times10^{4}$, except for the two phases, $\delta_\parallel$ (rad) and $\delta_\perp$ (rad), in which case the uncertainty is below $5\times10^{3}$. 
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Summary of the measured $ B^0_s\to { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \overline{ K}{} ^{*0} $ {\rm Swave} properties and their statistical and systematic uncertainties. When no value is given, it means an uncertainty below $5\times10^{4}$, except for the four phases related to the {\rm Swave} component, $\delta_{\rm S}$ (rad), in which case the uncertainty is below $5\times10^{3}$. The $ m_{ K^ \pi^+ }$ binning definition is identical to the one given in Table ???. 
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Summary of the measured values for the relative branching fractions and their statistical and systematic uncertainties. 
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Corrected angular acceptance weights for $K^\pi^+$ events lying in the first $ m_{ K^ \pi^+ }$ bin. The $\xi_{ij}$ weights are normalised with respect to the $\xi_{00}$ weight. 
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Statistical correlation matrix for the parameters from the angular fit. 
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Created on 18 January 2020.