Model-independent determination of the strong-phase difference between D⁰ and D̄⁰ → π⁺π⁻π⁺π⁻ decays

Measurements of the strong-phase difference between D⁰ and D̄⁰→π⁺π⁻π⁺π⁻ are performed in bins of phase space. The study exploits a sample of quantum-correlated DD̄ 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 γ (also denoted φ₃) in B^± → DK^±, D → π⁺π⁻π⁺π⁻ decays, and the binning schemes are designed to provide good statistical sensitivity to this parameter. The expected uncertainty on γ 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₊4π = 0.746 ± 0.010 ± 0.004 for the $C\!P$-even fraction of D⁰ → π⁺π⁻π⁺π⁻ decays, which is around 30% more precise than the previous best measurement of this quantity.