Measurement of the D → K−π+π+π− and D → K−π+π0 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+π0 are studied in a sample of quantum-correlated $$ D\overline{D} $$ D D ¯ pairs produced through the process e+e− → ψ(3770) → $$ D\overline{D} $$ D 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 D0 and a $$ {\overline{D}}^0 $$ 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 RK3π = $$ {0.52}_{-0.10}^{+0.12} $$ 0.52 − 0.10 + 0.12 and $$ {R}_{K{\pi \pi}^0} $$ R K ππ 0 = 0.78 ± 0.04, with values for the average strong-phase differences that are $$ {\delta}_D^{K3\pi }=\left({167}_{-19}^{+31}\right){}^{\circ} $$ δ D K 3 π = 167 − 19 + 31 ° and $$ {\delta}_D^{K{\pi \pi}^0}=\left({196}_{-15}^{+14}\right){}^{\circ} $$ δ D K ππ 0 = 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°.