Measurement of the D → K⁻ π⁺ π⁺ π⁻ and D → K⁻ π⁺ π⁰ coherence factors and average strong-phase differences in quantum-correlated DD¯ decays

The decays D → K⁻π⁺π⁺π⁻ and D → K⁻π⁺π⁰ are studied in a sample of quantum-correlated DD¯ pairs produced through the process e⁺e⁻ → ψ(3770) → DD¯ , exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb⁻¹. Here D indicates a quantum superposition of a D⁰ and a D¯ meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B⁻ → DK⁻ decays at the LHCb and Belle II experiments. The coherence factors are determined to be R_K3π = 0.52−0.10+0.12 and RKππ0 = 0.78 ± 0.04, with values for the average strong-phase differences that are δDK3π=(167−19+31)° and δDKππ0=(196−15+14)°, where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K⁻π⁺π⁺π⁻ to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6°. [Figure not available: see fulltext.]