Measurement of the time-integrated $C\!P$ asymmetry in $D^0\to K^- K^+$ decays

The time-integrated $C\!P$ asymmetry in the Cabibbo-suppressed decay $D^0\to K^-K^+$ is measured using proton-proton collision data, corresponding to an integrated luminosity of 5.7 fb$^{-1}$ collected at a center-of-mass energy of 13 TeV with the LHCb detector. The $D^0$ mesons are required to originate from promptly produced $D^{*+}\to D^0\pi^+$ decays and the charge of the companion pion is used to determine the flavor of the charm meson at production. The time-integrated $C\!P$ asymmetry is measured to be \begin{align*} \mathcal{A}_{C\!P}(K^-K^+) = \left[6.8 \pm 5.4 \text{ (stat)} \pm 1.6 \text{ (syst)} \right]\times 10^{-4}. \end{align*} The direct $C\!P$ asymmetries in $D^0\to K^- K^+$ and $D^0\to\pi^-\pi^+$ decays, $a_{K^-K^+}^{d}$ and $a_{\pi^-\pi^+}^{d}$, are derived by combining $\mathcal{A}_{C\!P} (K^-K^+)$ with the time-integrated $C\!P$ asymmetry difference, $\Delta \mathcal{A}_{C\!P} =\mathcal{A}_{C\!P} (K^-K^+)-\mathcal{A}_{C\!P} (\pi^-\pi^+)$, giving \begin{alignat*}{2} a_{K^-K^+}^{d} &= (\phantom{2}7.7 \pm 5.7) \times 10^{-4}, \end{alignat*} \begin{alignat*}{2} a_{\pi^-\pi^+}^{d} &= (23.2 \pm 6.1) \times 10^{-4}, \end{alignat*} with a correlation coefficient corresponding to $\rho=0.88$. The compatibility of these results with $C\!P$ symmetry is 1.4 and 3.8 standard deviations for $D^0\to K^- K^+$ and $D^0\to\pi^-\pi^+$ decays, respectively. This is the first evidence for direct $C\!P$ violation in a specific $D^0$ decay.