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

Abstract

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 the BESIII detector. We measure the asymmetry ${\mathcal{A}}_{K\pi }^{CP}$ of the branching fractions of $D\to K^{-}{\pi }^{+}$ in $CP$-odd and $CP$-even eigenstates to be $(12.7\pm 1.3\pm 0.7)\times 10^{-2}$. ${\mathcal{A}}_{K\pi }^{CP}$ can be used to extract the strong phase difference ${\delta }_{K\pi }$ between the doubly Cabibbo-suppressed process $\overline{D}{}^0\to K^{-}{\pi }^{+}$ and the Cabibbo-favored process $D^0\to K^{-}{\pi }^{+}$. Using world-average values of external parameters, we obtain $\cos {\delta }_{K\pi }=1.02\pm 0.11\pm 0.06\pm 0.01$. 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.

11 pages, 3 figures, accepted by PLB, minor changes from the last version

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