A measurement of the timedependent $ C\!P$ violating asymmetry in $ B ^0_ s \rightarrow \phi\phi$ decays is presented, along with measurements of the $ T$ odd tripleproduct asymmetries. Using a sample of protonproton collision data corresponding to an integrated luminosity of $5.0\,fb^{1} $ collected with the LHCb detector, a signal yield of approximately 8500 $ B ^0_ s \!\rightarrow \phi\phi$ decays is obtained. The $ C\!P$ violating phase is measured to be ${\phi_{ s }^{ s \overline s s } =0.07\pm0.13\mathrm{\,(stat)} \pm0.03\mathrm{\,(syst)} }\rm \,rad $. The tripleproduct asymmetries are measured to be ${A_U=0.000\pm0.012\mathrm{\,(stat)} \pm0.004\mathrm{\,(syst)} }$ and ${A_V=0.003\pm0.012\mathrm{\,(stat)} \pm0.004\mathrm{\,(syst)} }$. The results obtained are consistent with the hypothesis of $ C\!P$ conservation in $ b \rightarrow s \overline s s $ transitions. In addition, an improved limit on the branching fraction of the $ B ^0 \rightarrow \phi\phi$ decay is set, $\mathcal{B}( B ^0 \rightarrow \phi\phi)<2.4\times 10^{8}$ at 90\,% confidence level.
A fit to the 2011 (top left), 2012 (top right), 2015 (bottom left) and 2016 (bottom right) data, represented by the black points. Also shown are the results of the total fit (blue solid line), with the $ B ^0_ s \!\rightarrow \phi\phi$ (red dashed), the $\Lambda ^0_ b \rightarrow \phi p K ^ $ (magenta long dashed), and the combinatorial (blue short dashed) fit components. 
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Decay angles for the $ B ^0_ s \rightarrow \phi \phi$ decay, where $\theta_{1,2}$ is the angle between the $K^+$ track momentum in the $\phi_{1,2}$ meson rest frame and the parent $\phi_{1,2}$ momentum in the $ B ^0_ s $ rest frame, $\Phi$ is the angle between the two $\phi$ meson decay planes and $\hat{n}_{V_{1,2}}$ is the unit vector normal to the decay plane of the $\phi_{1,2}$ meson. 
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Angular acceptance found from simulated $ B ^0_ s \!\rightarrow \phi\phi$ decays (topleft) integrated over $\cos\theta_2$ and $\Phi$ as a function of $\cos\theta_1$, (topright) integrated over $\cos\theta_1$ and $\Phi$ as a function of $\cos\theta_2$, and (bottom) integrated over $\cos\theta_1$ and $\cos\theta_2$ as a function of $\Phi$. 
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Decaytime acceptances calculated from (left) $ B ^0_ s \rightarrow D ^_ s \pi ^+ $ and (right) $ B ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^{*0} $ decays. Superimposed are calculated analytical splines. 
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Onedimensional projections of the $ B ^0_ s \rightarrow \phi\phi$ fit for (topleft) decay time with binned acceptance, (topright) helicity angle $\Phi$ and (bottomleft and bottomright) cosine of the helicity angles $\theta_1$ and $\theta_2$. The backgroundsubtracted data are marked as black points, while the blue solid lines represent the projections of the best fit. The $ C\!P$ even $P$wave, the $ C\!P$ odd $P$wave and $S$wave combined with double $S$wave components are shown by the red long dashed, green short dashed and purple dotdashed lines, respectively. Fitted components are plotted taking in to account efficiencies in the time and angular observables. 
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Fit to the fourkaon invariant mass. The total PDF as described in the text is shown as a blue solid line, $ B ^0_ s \!\rightarrow \phi\phi$ as a red dashed line, $ B ^0 \rightarrow \phi \phi$ as a green dotted line, the $\Lambda ^0_ b \rightarrow \phi p K$ as a magenta longdashed line and the combinatorial background as a blue shortdashed line. 
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Results of the ${\rm CL}_s$ scan as a function of $N_{ B ^0 }$. The solid black line shows the observed ${\rm CL}_s$ distribution, while the dotted black line indicates the expected distribution. The green (yellow) band marks the $1\sigma$ ($2\sigma$) confidence region on the expected ${\rm CL}_s$. The $90\,(95)\,\%$ CL limit is indicated as a solid (dashed) red line. 
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Animated gif made out of all figures. 
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Coefficients of the timedependent terms and angular functions used in Eq. 2. Amplitudes are defined at $t=0$. 
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Angular coefficients, written in the same basis as the efficiency parameterisation. 
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Tagging performance of the opposite side (OS) and same side kaon (SSK) flavour taggers. 
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Results of the timedependent fit. Uncertainties shown do not include systematic contributions. 
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Correlation matrix associated with the result of the timedependent fit and relate to the statistical uncertainties. 
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Summary of systematic uncertainties for physics parameters in the timedependent measurement, where AA denotes angular acceptance, TA denotes time acceptance, and TR time resolution. 
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Summary of systematic uncertainties on $A_U$ and $A_V$. 
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Created on 20 April 2019.Citation count from INSPIRE on 20 April 2019.