$CP$-violating asymmetries from the decay-time distribution of prompt $D^0 \to K^+ K^-$ and $D^0 \to \pi^+\pi^-$ decays in the full $\mbox{LHCb}$ Run 1 data sample. Measurement using unbinned, acceptance corrected decay-time.

A study of indirect $CP$ violation in $D^0$ mesons is presented through a measurement of the asymmetry of the effective decay widths of $D^0$ and $\overline{D}^0$ mesons to $CP$ eigenstates. This observable, known as $A_{\Gamma}$, is measured with the $CP$ eigenstates $K^+ K^-$ and $\pi^+ \pi^-$ using data collected in $pp$ collisions by the LHCb experiment in 2012 with an integrated luminosity of $1.9\ \rm fb^{-1}$. The results are combined with a previously published LHCb measurement using this method for data collected in 2011 to yield average values of \begin{align*} A_{\Gamma}(D^0 \to K^+ K^-) = (-0.14 \pm0.37 \pm 0.10)\times 10^{-3}, \\ A_{\Gamma}(D^0\to \pi^+\pi^-) = ( \ 0.14\pm 0.63\pm 0.15)\times 10^{-3}, \end{align*} where the first quoted uncertainty is statistical, and the second systematic. The results are compatible with $CP$ conservation and with the Standard Model prediction.