The decays of $B_s^0$ and $\overline{B}_s^0$ mesons into the $J/\psi K^+K^$ final state are studied in the $K^+K^$ mass region above the $\phi(1020)$ meson in order to determine the resonant substructure and measure the $CP$violating phase, $\phi_s$, the decay width, $\Gamma_s$, and the width difference between light and heavy mass eigenstates, $\Delta\Gamma_s$. A decaytime dependent amplitude analysis is employed. The data sample corresponds to an integrated luminosity of $3{\rm fb}^{1}$ produced in 7 and 8 Tev $pp$ collisions at the LHC, collected by the LHCb experiment. The measurement determines $\phi_s = 119\pm107\pm34 {\rm mrad}$. A combination with previous LHCb measurements using similar decays into the $J/\psi \pi^+\pi^$ and $J/\psi\phi(1020)$ final states gives $\phi_s=1\pm37 {\rm mrad}$, consistent with the Standard Model prediction.
Definition of the helicity angles. 
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Fits to invariant mass distributions of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ combinations after subtraction of the two reflection backgrounds for (a) $m_{KK}<1.05$ $\mathrm{ Ge V}$ and (b) $m_{KK}>1.05$ $\mathrm{ Ge V}$ . Total fits are shown by solid (blue) lines, the signal by dashed (black) lines, and the combinatorial background by darkened regions. Note that the combinatorial background in (a) is too small to be easily visible. 
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Invariant mass squared of $K^+K^$ versus $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+$ for $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ candidates within $\pm15$ $\mathrm{ Me V}$ of the $ B ^0_ s $ mass peak. The high intensity $\phi(1020)$ resonance band is shown with a line (light green). 
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Scaled decaytime efficiency $\varepsilon_{\rm data}^{ B ^0_ s }(t)$ in arbitrary units (a.u.) for (a) the $\phi(1020)$ region and (b) the highmass region. 
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Efficiencies projected onto (a) $m_{KK}$, (b) $\cos \theta_{KK}$, (c) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ and (d) $\chi$ in arbitrary units (a.u.), obtained from simulation of $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ K ^ $ phasespace decays (points with error bars), while the curves show the parameterization from the efficiency model. 
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Projections of the fitting variables in the (left) lowmass ($\phi(1020)$) and (right) highmass regions shown by the solid (blue) curves. The points with error bars are the data. At the bottom of each figure the differences between the data and the fit divided by the uncertainty in the data are shown. 
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Fit projection of $m_{KK}$. The points represent the data; the resonances $\phi(1020)$, $f_2^\prime(1525)$, $\phi(1680)$ are shown by magenta, brown, and cyan longdashed curves, respectively; the Swave component is depicted by green longdashed curves; the other $f_2$ resonances are described by black solid curves; and the total fit by a blue solid curve. At the bottom the differences between the data and the fit divided by the uncertainty in the data are shown. 
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The $K^+K^$ mass dependence of the spherical harmonic moments of $\cos \theta_{KK}$ in the region of the $\phi(1020)$ resonance after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. 
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The $K^+K^$ mass dependence of the spherical harmonic moments of $\cos \theta_{KK}$ above the $\phi(1020)$ resonance region after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. 
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Animated gif made out of all figures. 
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BreitWigner resonance parameters. 
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Fit results for the $ B ^0_ s $ decay observables in the high $m_{KK}$ region. 
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Fit results of the resonant structure. 
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Fitted phase differences between two transversity states (statistical uncertainty only). Here the symbol $\phi$ refers to the components of the $\phi(1020)$ meson. 
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Absolute systematic uncertainties for the physics parameters determined from the high $m_{KK}$ region compared to the corresponding statistical uncertainty. Here $M_0$ and $\Gamma_0$ refer to the uncertainties on the $f_2^\prime(1525)$ resonance mass and width. 
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Combined systematic and statistical uncertainties in the fit fractions using an absolute scale where the numbers are in units of %. "Res. modelling" refers to resonance modelling. 
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The correlation matrix from the highmass region fit, taking into account both statistical and systematic uncertainties. 
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The correlation matrix taking into account both statistical and systematic uncertainties for the combination of the three measurements $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ for $m_{KK}>1.05$ GeV, $m_{KK}<1.05$ GeV, and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$. 
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Created on 18 January 2020.