$CP$-violating asymmetries from the decay-time distribution of prompt $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays in the full LHCb Run~1 data sample. Measurement using yield asymmetries in bins of decay time.

Time-dependent $CP$ asymmetries in the decay rates of the singly Cabibbo-suppressed decays $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ are measured in $pp$ collision data at centre-of-mass energies of $7$ and $8\,\mathrm{TeV}$ collected by the LHCb detector, corresponding to an integrated luminosity of $3\,\mathrm{fb}^{-1}$. The strong-interaction decay $D^{*+} \to D^0\pi^+$ is used to infer the flavour of the $D^0$ mesons at production. The asymmetries in effective decay widths between $D^0$ and $\overline{D}^0$ decays, sensitive to indirect $CP$ violation, are measured to be \begin{align*} A_\Gamma(D^0 \to K^+K^-) &= (-0.30 \pm 0.32 \pm 0.14)\times 10^{-3},\\ A_\Gamma(D^0 \to \pi^+\pi^-) &=(\phantom{-}0.46 \pm 0.58 \pm 0.16)\times 10^{-3}, \end{align*} where the first quoted uncertainty is statistical, and the second systematic. These measurements are consistent with $CP$ conservation and improve by nearly a factor two the previous world leading measurements, also obtained by LHCb using the 2011 subsample of the current data.