A search for time-integrated CP violation in $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ decays

The preliminary results of a search for time-integrated $CP$ violation in $D^0\rightarrow K^-K^+$ and in $D^0\rightarrow \pi^-\pi^+$ decays performed with a dataset corresponding to an integrated luminosity of $1.0~\mathrm{fb}^{-1}$ collected by LHCb in 2011 are presented. The flavour of the initial state ($D^0$ or $\overline{D}^0$) is identified by the charge of the soft pion ($\pi^+_s$) in the $D^{*+}\rightarrow D^0\pi_s^+$ decay. The difference in $CP$ asymmetry between the $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ modes, $\Delta A_{CP} \equiv A_{CP}(K^-K^+)-A_{CP}(\pi^-\pi^+)$ is measured to be $\Delta A_{CP} = (-0.34\pm 0.15 \pm 0.10 )\%$, where the first uncertainty is statistical and the second systematic.