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A search for $CP$ violation using $T$-odd correlations is performed using thefour-body $D^0 \to K^+K^-\pi^+\pi^-$ decay, selected from semileptonic $B$decays. The data sample corresponds to integrated luminosities of$1.0\,\text{fb}^{-1}$ and $2.0\,\text{fb}^{-1}$ recorded at the centre-of-massenergies of 7 TeV and 8 TeV, respectively. The $CP$-violating asymmetry$a_{CP}^{T\text{-odd}}$ is measured to be $(0.18\pm 0.29\text{(stat)}\pm0.04\text{(syst)})\%$. Searches for $CP$ violation in different regions ofphase space of the four-body decay, and as a function of the $D^0$ decay time,are also presented. No significant deviation from the $CP$ conservationhypothesis is found.

Search for $CP$ violation using $T$-odd correlations in $D^0 \to K^+K^-\pi^+\pi^-$ decays