Timeintegrated $CP$ asymmetries in $D^0$ decays to the final states $K^ K^+$ and $\pi^ \pi^+$ are measured using protonproton collisions corresponding to $3\mathrm{ fb}^{1}$ of integrated luminosity collected at centreofmass energies of $7\mathrm{ Te V}$ and $8\mathrm{ Te V}$. The $D^0$ mesons are produced in semileptonic $b$hadron decays, where the charge of the accompanying muon is used to determine the initial flavour of the charm meson. The difference in $CP$ asymmetries between the two final states is measured to be \begin{align} \Delta A_{CP} = A_{CP}(K^K^+)A_{CP}(\pi^\pi^+) = (+0.14 \pm 0.16\mathrm{ (stat)} \pm 0.08\mathrm{ (syst)})\% \ . \nonumber \end{align} A measurement of $A_{CP}(K^K^+)$ is obtained assuming negligible $CP$ violation in charm mixing and in Cabibbofavoured $D$ decays. It is found to be \begin{align} A_{CP}(K^K^+) = (0.06 \pm 0.15\mathrm{ (stat)} \pm 0.10\mathrm{ (syst)}) \% \ ,\nonumber \end{align} where the correlation coefficient between $\Delta A_{CP}$ and $A_{CP}(K^K^+)$ is $\rho=0.28$. By combining these results, the $CP$ asymmetry in the $D^0\rightarrow\pi^\pi^+$ channel is $A_{CP}(\pi^\pi^+)=(0.20\pm0.19\mathrm{ (stat)}\pm0.10\mathrm{ (syst)})\%$.
Invariant mass distributions for muontagged (a) $ D ^0 \rightarrow K ^ K ^+ $ , (b) $ D ^0 \rightarrow \pi ^ \pi ^+ $ and (c) $ D ^0 \rightarrow K ^ \pi ^+ $ candidates and for prompt (d) $ D ^+ \rightarrow K ^ \pi ^+ \pi ^+ $ and (e) $ D ^+ \rightarrow \overline{ K }{} {}^0 \pi ^+ $ candidates. The results of the fits are overlaid. 
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Raw asymmetry in the $ D ^+ \rightarrow \overline{ K }{} {}^0 \pi ^+ $ decay shown for (a) long and (b) downstream $ K ^0_{\rm\scriptscriptstyle S}$ candidates versus the $ K ^0_{\rm\scriptscriptstyle S}$ decay time in units of its lifetime. The long $ K ^0_{\rm\scriptscriptstyle S}$ candidates are reconstructed in the full data set, while the downstream $ K ^0_{\rm\scriptscriptstyle S}$ candidates are reconstructed in the 2012 data only. The predicted effect from the $ K ^0$ asymmetry, $ A_D( K ^0 ) $, is also shown. An overall shift is applied to this prediction to account for $ D ^+$ production and pion detection asymmetries (note that the unshifted $ A_D( K ^0 )$ at $t=0$ is zero). 
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Measured $ K ^ \pi ^+ $ detection asymmetry as a function of the kaon momentum. The shaded band indicates the average asymmetry integrated over the bins. There is a correlation between the data points due to the overlap between the $ D ^+ \rightarrow \overline{ K }{} {}^0 \pi ^+ $ samples used for each bin. 
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Raw asymmetry, without background subtraction, as a function of the invariant mass for (a) the $ D ^0 \rightarrow K ^ K ^+ $ candidates and (b) the $ D ^0 \rightarrow \pi ^ \pi ^+ $ candidates for the $\Delta A_{ C P }$ selection. The result from the fit is overlaid. 
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(a) $\Delta A_{ C P }$ and (b) $ A_{ C P }( K ^ K ^+ )$ as a function of the data taking period. The 2011 data are divided into four periods and the 2012 data into six periods. The error bars indicate the statistical uncertainty, the shaded bands show the averages for 2011 and 2012, and the (red) line shows the overall $ C P$ asymmetry. 
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Animated gif made out of all figures. 
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Number of signal decays determined from fits to the invariant mass distributions. 
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Values of the parameters used to calculate the $ K ^0$ asymmetry [21,25]. 
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Asymmetries (in %) entering the calculation of the $ K ^ \pi ^+ $ detection asymmetry for the two magnet polarities, and for the mean value. The correction for the $ K ^0$ asymmetry is applied in the bottom row. The mean values in the last column are obtained first by taking the arithmetic average over the magnet polarities and then by taking the weighted averages of the 2011 and 2012 data sets. The uncertainties are statistical only. 
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Asymmetries (in %) used in the calculation of $\Delta A_{ C P }$ for the two magnet polarities. The values for $\Delta A_{ C P }$ are corrected for the mistag probability. The mean values in the last column are obtained first by taking the arithmetic average over the magnet polarities and then by taking the weighted averages of the 2011 and 2012 data sets. The uncertainties are statistical only. 
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Asymmetries (in %) used in the calculation of $ A_{ C P }( K ^ K ^+ )$ for the two magnet polarities. The values for $ A_{ C P }( K ^ K ^+ )$ are corrected for the mistag probability. The mean values in the last column are obtained first by taking the arithmetic average over the magnet polarities and then by taking the weighted averages of the 2011 and 2012 data sets. The uncertainties are statistical only. 
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Contributions to the systematic uncertainty of $\Delta A_{ C P }$ and $ A_{ C P }( K ^ K ^+ )$ . 
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Supplementary material full pdf 
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This ZIP file contains supplemetary material for the publication LHCbPAPER2014013. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in variuous formats 
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Created on 11 November 2019.