A measurement of the timeintegrated $CP$ asymmetry in $D^0\rightarrow K^0_S K^0_S$ decays is reported. The data correspond to an integrated luminosity of about $2$ fb$^{1}$ collected in 20152016 by the LHCb collaboration in $pp$ collisions at a centreofmass energy of $13$ TeV. The $D^0$ candidate is required to originate from a $D^{\ast +} \rightarrow D^0 \pi^+$ decay, allowing the determination of the flavour of the $D^0$ meson using the pion charge. The $D^0 \rightarrow K^{+}K^{}$ decay, which has a well measured $CP$ asymmetry, is used as a calibration channel. The $CP$ asymmetry for $D^0\rightarrow K^0_S K^0_S$ is measured to be \begin{equation*} \mathcal{A}^{CP}(D^0\rightarrow K^0_S K^0_S) = (4.3\pm 3.4\pm 1.0)\%, \end{equation*} where the first uncertainty is statistical and the second is systematic. This result is combined with the previous LHCb measurement at lower centreofmass energies to obtain \begin{equation*} \mathcal{A}^{CP}(D^0\rightarrow K^0_S K^0_S) = (2.3\pm 2.8\pm 0.9)\%. \end{equation*}
Exchange (left) and penguin annihilation (right) diagrams contributing to the $ D ^0 \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} K ^0_{\mathrm{ \scriptscriptstyle S}} $ amplitude. Based on Ref. [5]. 
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Twodimensional distribution of the logarithm of the $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ flight distance significance ($\log \chi^2_{\text{FD}} $) for the two $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ candidates in the LL subsample of $ D ^0 \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} K ^0_{\mathrm{ \scriptscriptstyle S}} $ decays. The $ D ^0 \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} K ^0_{\mathrm{ \scriptscriptstyle S}} $ signal can be observed in the upper right region of the plot. The contour corresponds to Eq. 6. 
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Results of fits to $\Delta m$ distributions of $ D ^0 \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} K ^0_{\mathrm{ \scriptscriptstyle S}} $ candidates for MagUp magnet polarity. The fit to (a) $D^{\ast +} \rightarrow D ^0 \pi ^+ $ and (b) $D^{\ast } \rightarrow \overline{ D }{} {}^0 \pi ^ $ candidates for the LL sample and the fit to (c) $D^{\ast +} \rightarrow D ^0 \pi ^+ $ and (d) $D^{\ast } \rightarrow \overline{ D }{} {}^0 \pi ^ $ candidates for the LD sample are shown. The black crosses represent the data points, the solid blue curve is the total fit function, and the dashed blue curve is the background component of the fit. 
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Results of fits to $\Delta m$ distributions of $ D ^0 \rightarrow K^+K^$ candidates for the MagUp magnet polarity. The fits to (a) $D^{\ast +} \rightarrow D ^0 \pi ^+ $ candidates and (b) $D^{\ast } \rightarrow \overline{ D }{} {}^0 \pi ^ $ candidates are shown. The black points represent the data, the dashed blue and solid blue curves represent the background component and the total fit function, respectively. 
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Values of $ {\Delta\mathcal{A}}^{\mathcal{C}_{P} }$ obtained for both magnet polarities on the LL and LD samples, along with the average of these measurements. Only statistical uncertainties are shown. 
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Animated gif made out of all figures. 
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Fit results on the $ D ^0 \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} K ^0_{\mathrm{ \scriptscriptstyle S}} $ LL and LD samples for each magnet polarity, where $N_{\mathrm{obs}}$ represents the number of candidates fitted. The purity is determined in the range $ 144.5 < \Delta m < 146.5\, {\mathrm{\,MeV\!/}c^2} $. For each sample, a $\chi^2 $ test statistic for the fitted model and binned data for positively and negatively charged candidates is constructed. The quantity $\mathcal{P}_{\rm fit}$ is the probability of observing a $\chi^2 $ value greater than that observed in the fit to real data, determined using simulated pseudoexperiments sampled from the fitted model. 
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Systematic uncertainties on the quantities $ {\mathcal{A}}^{\mathrm{raw}}$ and $\Delta {\mathcal{A}}^{\mathcal{C}_{P} } $. The total systematic uncertainties in the last row are obtained by summing the corresponding contributions in each column in quadrature. Uncertainties are expressed in units of $10^{3}$. 
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Created on 11 December 2018.Citation count from INSPIRE on 11 December 2018.