Decays of $B_{s}^{0}$ and $\overline{B}{}_{s}^{0}$ mesons into $J/\psi\pi^+\pi^$ final states are studied in a data sample corresponding to 1.9 fb$^{1}$ of integrated luminosity collected with the LHCb detector in 13 TeV $pp$ collisions. A timedependent amplitude analysis is used to determine the finalstate resonance contributions, the $CP$violating phase $\phi_s=0.057\pm 0.060\pm 0.011$ rad, the decaywidth difference between the heavier mass $B_{s}^{0}$ eigenstate and the $B^{0}$ meson of $0.050\pm 0.004\pm 0.004$ ps$^{1}$, and the $CP$violating parameter $\lambda=1.01_{0.06}^{+0.08}\pm0.03$, where the first uncertainty is statistical and the second systematic. These results are combined with previous LHCb measurements in the same decay channel using 7 TeV and 8 TeV $pp$ collisions obtaining $\phi_s =0.002\pm0.044\pm0.012$ rad, and $\lambda =0.949\pm0.036\pm0.019$.
Results of the simultaneous fit to the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi\pi$ mass distributions RS (black points) and WS (grey points) samples. The solid (blue) curve shows the fit to the RS sample, the long dashed (red) curve shows the signal, the dotdashed (magenta) curve shows $ B ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi ^+ \pi ^ $ decays, the dotlongdashed (brown) curve shows the combinatorial background, the dotted (black) curve shows the sum of $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \eta^\prime$ and $\Lambda ^0_ b $ background, while the dotdotdashed (green) curve shows the fit to WS sample. 
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Overall efficiency normalized to unity for (a) $m_{\pi\pi}$ , (b) $\cos \theta_{\pi\pi}$ , (c) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ and (d) $\chi$ observables. The points with error bars are from the $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi ^+ \pi ^ $ simulation, while the curves show the projection of the efficiency function. 
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Overall efficiency for (a) $m_{\pi\pi}$ vs $\cos \theta_{\pi\pi}$ and (b) $m^2_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi ^+ }$ vs $m^2_{\pi\pi}$. The inefficiency is at the kinematic boundary of $m^2_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+}$ where the pion is almost at rest in the $ B ^0_ s $ frame. 
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Projections of the angular and decaytime variables with the fit result overlaid. The points (black) show the data and the curves (blue) the fits. 
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Data distribution of $m_{\pi\pi}$ with the projection of the Solution I fit result overlaid. The data are described by the points (black) with error bars. The solid (blue) curve shows the overall fit. 
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Animated gif made out of all figures. 
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Tagging efficiency, $\varepsilon_{\rm tag}$, and tagging power given as the efficiency times dilution squared, $\varepsilon_{\rm tag}D^2$, where $D=(12\omega)$ for each category and the total. The uncertainties on $\varepsilon_{\rm tag}$ are statistical only, and those for $\varepsilon_{\rm tag}D^2$ contain both statistical and systematic components. 
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Resonance parameters. 
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Likelihoods of various resonance model fits. Positive or negative interferences (Int) among the contributing resonances are indicated. The Solutions are indicated by \#. 
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Fit results for the $ C P$ violating parameters for Solution I. The first uncertainties are statistical, and the second systematic. The last three columns show the statistical correlation coefficients for the three parameters. 
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Fit results of the resonant structure for both Solutions I and II. These results do not supersede those in Ref. [27] for the resonant fractions because no systematic uncertainties are quoted. The sum of fit fraction is not necessary 100% due to possible interferences between resonances with the same spin. 
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Absolute systematic uncertainties for the physics parameters. 
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Created on 11 July 2020.