Model-independent determination of the strong-phase difference between D⁰ and D⁰ ^+^-^+^- decays

Measurements of the strong-phase difference between D⁰ and D⁰^+^-^+^- are performed in bins of phase space. The study exploits a sample of quantum-correlated DD mesons collected by the BESIII experiment in e^+e^- collisions at a center-of-mass energy of 3. 773~GeV, corresponding to an integrated luminosity of 2. 93~fb^-1. Here, D denotes a neutral charm meson in a superposition of flavor eigenstates. The reported results are valuable for measurements of the C\!P-violating phase (also denoted ₃) in B^ DK^, D ^+^-^+^- decays, and the binning schemes are designed to provide good statistical sensitivity to this parameter. The expected uncertainty on arising from the precision of the strong-phase measurements, when applied to very large samples of B-meson decays, is around 1. 5^ or 2^, depending on the binning scheme. The binned strong-phase parameters are combined to give a value of F_+^4 = 0. 746 0. 010 0. 004 for the C\!P-even fraction of D⁰ ^+^-^+^- decays, which is around 30\% more precise than the previous best measurement of this quantity.