Measurement of the D → K − π + π + π − and D → K − π + π 0 coherence factors and average strong-phase differences in quantum-correlated $D\overline{D}$ decays

The decays D → K − π + π + π − and D → K − π + π 0 are studied in a sample of quantum-correlated $D\overline{D}$ pairs produced through the process e + e − → ψ(3770) → $D\overline{D}$ , 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 D 0 and a ${\overline{D}}^{0}$ 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 ${R}_{K{\mathrm{\pi \pi }}^{0}}$ = 0.78 ± 0.04, with values for the average strong-phase differences that are ${\delta }_{D}^{K3\pi }=\left({167}_{-19}^{+31}\right)°$ and ${\delta }_{D}^{K{\mathrm{\pi \pi }}^{0}}=\left({196}_{-15}^{+14}\right)°$ , 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°.