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