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

A search for $CP$ violation using $T$-odd correlations is performed using the four-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-mass energies of 7 TeV and 8 TeV, respectively. The $CP$-violating asymmetry $a_{CP}^{Ttext{-odd}}$ is measured to be $(0.18pm 0.29text{(stat)}pm 0.04text{(syst)})%$. Searches for $CP$ violation in different regions of phase space of the four-body decay, and as a function of the $D^0$ decay time, are also presented. No significant deviation from the $CP$ conservation hypothesis is found.