Search for $C\!P$ violation in $D^0\rightarrow K^+K^-$ decays using $D^0\rightarrow K_1^0\pi^+\pi^-$ decays as calibration mode

A search for time-integrated violation of the charge-parity ($C\!P$) symmetry, $\mathcal{A}_{C\!P}^{KK}$ , in the $D^0\rightarrow K^+K^-$ decay is performed at the LHCb experiment using proton-proton collision data recorded from 2016 to 2018 at a center-of-mass energy of $13\,\textrm{TeV}$, corresponding to an integrated luminosity of $5.4\,\textrm{fb}^{-1}$. The $D^0$ meson is required to originate from a $D^{*}(2010)^{+}\rightarrow D^0\pi^+_{\textrm{tag}}$ decay, such that its flavor at production is identified by the charge of the accompanying pion. Nuisance asymmetries are subtracted using a sample of $D^{*}(2010)^{+}\rightarrow D^0(\rightarrow K_1^0\pi^+\pi^-)\pi^+_{\textrm{tag}}$ decays, where $K_1^0$ represents the $C\!P$-even neutral kaon eigenstate. The blinded asymmetry is measured to be $$\mathcal{A}_{C\!P}^{KK} = [xx \pm 5.1 \pm 1.5]\times 10^{-4},$$ where the first uncertainty is statistical, and the second is systematic. This is the world's most precise measurement of this quantity to date. The combination of this measurement of $\mathcal{A}_{C\!P}^{KK}$ with previous measurements of the same quantity, the time-integrated $C\!P$ asymmetry difference, $\Delta A_{C\!P} = \mathcal{A}_{C\!P}^{KK} - \mathcal{A}_{C\!P}^{\pi\pi}$, and the time-dependent $C\!P$ asymmetry, $\Delta Y$, measured with $D^0\rightarrow K^+K^-$ and $D^0\rightarrow \pi^+\pi^-$ decays, the $C\!P$ asymmetries in the $D^0\rightarrow K^+K^-$ and $D^0\rightarrow \pi^+\pi^-$ decays, $a^d_{KK}$ and $a^d_{\pi\pi}$, gives $$a^d_{KK} = [yy\pm3.3]\times 10^{-4},$$$$a^d_{\pi\pi} = [zz\pm4.3]\times 10^{-4},$$ where the uncertainties include systematic and statistical contributions. Under the hypothesis that the central value of the new measurement of $\mathcal{A}_{C\!P}^{KK}$ presented here is equal to the world average, the measured value of $a^d_{\pi\pi}$ would show a departure from zero at the level of 5 standard deviations, providing the first observation of $C\!PV$ in a single decay channel of a charmed meson.