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

Abstract

The decays D → K⁻π⁺π⁺π⁻ and D → K⁻π⁺π⁰ 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 D⁰ 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 $R_{K{\mathit{\pi \pi }}^0}$ = 0.78 ± 0.04, with values for the average strong-phase differences that are ${\delta }_D^{K3\pi }=\left({167}_{-19}^{+31}\right)°$ and ${\delta }_D^{K{\mathit{\pi \pi }}^0}=\left({196}_{-15}^{+14}\right)°$, 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°.