Study of the decaysD→K3π

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Abstract

We report measurements of the decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, and ${D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ from Fermilab photoproduction experiment E691. A complete resonant substructure analysis is used to determine the relative fractions and phases of amplitudes contributing to the decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, and ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$.

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