Improved measurements of the coherence factors and strong-phase differences in $D\to K^-\pi^+\pi^+\pi^-$ and $D\to K^-\pi^+\pi^0$ with quantum-correlated $D\bar{D}$ decays

Abstract

Improved measurements of the coherence factors and strong-phase differences in $D\to K^-\pi^+\pi^+\pi^-$ and $D\to K^-\pi^+\pi^0$ decays are reported, using quantum-correlated $D\bar{D}$ pairs produced in $e^+e^-$ annihilation at a center-of-mass energy of $3.773\,\mathrm{GeV}$, where $D$ denotes a quantum superposition of the flavour-specific $D^{0}$ and $\bar{D}^{0}$ mesons. The analysis employs a dataset collected by the BESIII experiment, corresponding to an integrated luminosity of $7.93~\rm fb^{-1}$. 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 $\gamma$ of the Cabibbo-Kobayashi-Maskawa Unitarity Triangle in the LHCb and Belle II experiments. The coherence factors are determined to be $R_{K3\pi}=0.51\pm0.04$ and $R_{K\pi\pi^0}=0.75\pm0.03$, and the strong-phase differences are $\delta_D^{K3\pi}=\left(182^{+14}_{-13}\right)^\circ$ and $\delta_D^{K\pi\pi^0}=\left(209^{+7}_{-8}\right)^\circ$, where the uncertainties include both statistical and systematic contributions. For $D\to K^-\pi^+\pi^+\pi^-$, the parameters have been further determined in four phase-space bins with improved precision compared to the previous BESIII results. The uncertainty on future $\gamma$ measurements from the knowledge of $D\to K^-\pi^+\pi^+\pi^-$ parameters is expected to be reduced to approximately 3.5$^\circ$.