Improved measurements of the coherence factors and strong-phase differences in D → K−π+π+π− and D → K−π+π0 with quantum-correlated $$ D\overline{D} $$ decays

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A bstract Improved measurements of the coherence factors and strong-phase differences in D → K − π + π + π − and D → K − π + π 0 decays are reported, using quantum-correlated $$ D\overline{D} $$ D D ¯ pairs produced in e + e − annihilation at a center-of-mass energy of 3 . 773 GeV, where D denotes a quantum superposition of the flavour-specific D 0 and $$ {\overline{D}}^0 $$ D ¯ 0 mesons. The analysis employs a dataset collected by the BESIII experiment, corresponding to an integrated luminosity of 7 . 93 fb − 1 . The observables sensitive to the coherence factors and strong-phase differences are measured by reconstructing one D meson in the signal mode and the other in a tag mode. These parameters provide essential inputs to the measurement of the angle γ of the Cabibbo-Kobayashi-Maskawa Unitarity Triangle in the LHCb and Belle II experiments. The coherence factors are determined to be R K 3 π = 0.51 ± 0.04 and $$ {R}_{K\pi {\pi}^0}=0.75\pm 0.03 $$ R Kπ π 0 = 0.75 ± 0.03 , and the strong-phase differences are $$ {\delta}_D^{K3\pi }={\left({182}_{-13}^{+14}\right)}^{\circ } $$ δ D K 3 π = 182 − 13 + 14 ∘ and $$ {\delta}_D^{K\pi {\pi}^0}={\left({209}_{-8}^{+7}\right)}^{\circ } $$ δ D Kπ π 0 = 209 − 8 + 7 ∘ , where the uncertainties include both statistical and systematic contributions. For D → K − π + π + π − , the parameters have been further determined in four phase-space bins with improved precision compared to the previous BESIII results. The uncertainty on future γ measurements from the knowledge of D → K −

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