| Summary: | Crucial inputs for a variety of CP-violation studies can be determined through the analysis of pairs of quantum-entangled neutral D mesons, which are produced in the decay of the ψð3770Þ resonance. The relative strong-phase parameters between D0 and D¯ 0 in the decays D0 → K0 S;Lπþπ− are studied using 2.93 fb−1 of eþe− annihilation data delivered by the BEPCII collider and collected by the BESIII detector at a center-of-mass energy of 3.773 GeV. Results are presented in regions of the phase space of the decay. These are the most precise measurements to date of the strong-phase parameters in D → K0 S;Lπþπ− decays. Using these parameters, the associated uncertainty on the Cabibbo-Kobayashi-Maskawa angle γ=ϕ3 is expected to be between 0.7° and 1.2° for an analysis using the decay B → DK, D → K0Sπþπ−, where D represents a superposition of D0 and D¯ 0 states. This is a factor of 3 smaller than that achievable with previous measurements. Furthermore, these results provide valuable input for charm-mixing studies, other measurements of CP violation, and the measurement of strong-phase parameters for other D-decay modes.
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