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We study $D^0\overline{D}{}^0$ pairs produced in $e^+e^-$ collisions at$\sqrt{s}=3.773$ GeV using a data sample of 2.92 fb$^{-1}$ collected with theBESIII detector. We measure the asymmetry $\mathcal{A}^{CP}_{K\pi}$ of thebranching fractions of $D \to K^-\pi^+$ in $CP$-odd and $CP$-even eigenstatesto be $(12.7\pm1.3\pm0.7)\times10^{-2}$. $\mathcal{A}^{CP}_{K\pi}$ can be usedto extract the strong phase difference $\delta_{K\pi}$ between the doublyCabibbo-suppressed process $\overline{D}{}^{0}\to K^-\pi^+$ and theCabibbo-favored process $D^0\to K^- \pi^+$. Using world-average values ofexternal parameters, we obtain $\cos\delta_{K\pi} = 1.02\pm0.11\pm0.06\pm0.01$.Here, the first and second uncertainties are statistical and systematic,respectively, while the third uncertainty arises from the external parameters.This is the most precise measurement of $\delta_{K\pi}$ to date.

Measurement of the $D\to K^-\pi^+$ strong phase difference in $\psi(3770)\to D^0\overline{D}{}^0$