A measurement of the decay time dependent CPviolating asymmetry in $B_s^0 \to \phi\phi$ decays is presented, along with measurements of the $T$odd tripleproduct asymmetries. In this decay channel, the CPviolating weak phase arises from the interference between $B_s^0$$\bar{B}_s^0$ mixing and the loopinduced decay amplitude. Using a sample of protonproton collision data corresponding to an integrated luminosity of $3.0\, fb^{1}$ collected with the LHCb detector, a signal yield of approximately 4000 $B_s^0 \to \phi\phi$ decays is obtained. The CPviolating phase is measured to be ${\phi_s =0.17\pm0.15\mathrm{\,(stat)}\pm0.03\mathrm{\,(syst)}}$ rad. The tripleproduct asymmetries are measured to be ${A_U=0.003\pm0.017\mathrm{\,(stat)}\pm0.006\mathrm{\,(syst)}}$ and ${A_V=0.017\pm0.017\mathrm{\,(stat)}\pm0.006\mathrm{\,(syst)}}$. Results are consistent with the hypothesis of CP conservation.
Fourkaon invariant mass distributions for the (left) 2011 and (right) 2012 datasets. The data points are represented by the black markers. Superimposed are the results of the total fit (red solid line), the $ B ^0_ s \!\to \phi\phi$ (red long dashed), the $ B ^0 \to\phi K ^{*0} $ (blue dotted), the $\Lambda ^0_ b \to\phi p K ^ $ (green shortdashed), and the combinatoric (purple dotted) fit components. 
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Decay angles for the $ B ^0_ s \rightarrow \phi \phi$ decay, where the $K^+$ momentum in the $\phi_{1,2}$ rest frame and the parent $\phi_{1,2}$ momentum in the rest frame of the $ B ^0_ s $ meson span the two $\phi$ meson decay planes, $\theta_{1,2}$ 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 \!\to \phi\phi$ events (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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Decay time acceptance (left) calculated using $ B ^0_ s \to D ^_ s \pi ^+ $ data events, and (right) comparing $ B ^0_ s \!\to \phi\phi$ and $ B ^0_ s \to D ^_ s \pi ^+ $ simulation, where $ B ^0_ s \to D ^_ s \pi ^+ $ events are reweighted to match the distribution of the minimum $p_{\rm T}$ of the final state particles in $ B ^0_ s \!\to \phi\phi$ decays. 
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Onedimensional projections of the $ B ^0_ s \to \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 black 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 blue dotted lines, respectively. 
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Profile loglikelihood for the $\phi_s$ parameter. 
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Backgroundsubtracted distributions of the (left) $U$ and (right) $V$ observables for the 2011 and 2012 datasets and restricted to the mass range $5246.8<m_{ K ^+ K ^ K ^+ K ^ }<5486.8 {\mathrm{\,Me V\!/}c^2} $. The 2011 distributions are scaled to have the same area as the 2012 distributions. 
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Animated gif made out of all figures. 
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Coefficients of the time dependent terms and angular functions used in Eq. 2. Amplitudes are defined at $t=0$. 
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Tagging efficiency ($\epsilon_{\rm tag}$), effective dilution ($\mathcal{D}$), and tagging power ($\epsilon \mathcal{D}^2$), as estimated from the data for events tagged containing information from OS algorithms only, SSK algorithms only, and information from both algorithms. Quoted uncertainties include both statistical and systematic contributions. 
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Results of the decay time dependent fit. 
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$S$wave and double $S$wave results of the decay time dependent fit for the three regions identified in Sec. 8.1, where $M_{}$ indicates the region with both twokaon invariant masses smaller than the known $\phi$ mass, $M_{+}$ the region with one smaller and one larger, and $M_{++}$ indicates the region with both twokaon invariant masses larger than the known $\phi$ mass. 
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Correlation matrix associated with the result of the decay time dependent fit. Correlations with a magnitude greater than 0.5 are shown in bold. 
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Summary of systematic uncertainties for physics parameters in the decay time dependent measurement, where AA denotes angular acceptance. 
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{} Systematic uncertainties on the tripleproduct asymmetries $A_U$ and $A_V$. The total uncertainty is the sum in quadrature of the larger of the two components for each source. 
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Created on 20 April 2019.Citation count from INSPIRE on 25 April 2019.