Novel measurement of the strong-phase difference between $ {D}^{0}\to {K}^{-}{\pi }^{+}$ and $ {\overline{D}}^{0}\to {K}^{-}{\pi }^{+}$ decays using $ C$-even and $ C$-odd quantum-correlated $ D\overline{D}$ pairs

A novel measurement technique of strong-phase differences between the decay amplitudes of $ {D}^{0}$ and $ {\overline{D}}^{0}$ mesons is introduced which exploits quantum-correlated $ D\overline{D}$ pairs produced by $ {e}^{+}{e}^{-}$ collisions at energies above the $ \psi (3770)$ production threshold, where $ D\overline{D}$ pairs are produced in both even and odd eigenstates of the charge-conjugation symmetry. Employing this technique, the first determination of a $ {D}^{0}–{\overline{D}}^{0}$ relative strong phase is reported with such data samples. The strong-phase difference between $ {D}^{0}\to {K}^{-}{\pi }^{+}$ and $ {\overline{D}}^{0}\to {K}^{-}{\pi }^{+}$ decays, $ {\delta }_{K\pi }^{D}$, is measured to be $ {\delta }_{K\pi }^{D}={({192.8}_{-12.4-2.4}^{+11.0+1.9})}^{\circ }$, using a dataset corresponding to an integrated luminosity of $ 7.13\text{}\text{}{\mathrm{fb}}^{-1}$ collected at center-of-mass energies between 4.13–4.23 GeV by the BESIII experiment.