Resonant substructure inK−π+π+π−decays ofD0mesons

We determine the resonant substructure of ${\mathit{D}}^{0}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$ decays using a five-dimensional maximum-likelihood technique to extract the relative fractions and phases of the amplitudes contributing to this final state. We find that two-body decay modes account for at least 76% of all decays. We obtain branching ratios for several decay modes including B(${\mathit{D}}^{0}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}}$${\mathit{a}}_{1}^{+}$) =(9.0\ifmmode\pm\else\textpm\fi{}0.9\ifmmode\pm\else\textpm\fi{}1.7)%, B(${\mathit{D}}^{0}$\ensuremath{\rightarrow}K\ifmmode\bar\else\textasciimacron\fi{} $^{\mathrm{*}0}\mathrm{\ensuremath{\rho}}^{0}$)=(1.9\ifmmode\pm\else\textpm\fi{}0.3\ifmmode\pm\else\textpm\fi{}0.7)%, and B(${\mathit{D}}^{0}$\ensuremath{\rightarrow}${\mathit{K}}_{1}$(1270${)}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{+}$) =(1.8\ifmmode\pm\else\textpm\fi{}0.5 \ifmmode\pm\else\textpm\fi{}0.8)%. For the decay mode ${\mathit{D}}^{0}$\ensuremath{\rightarrow}K\ifmmode\bar\else\textasciimacron\fi{} $^{\mathrm{*}0}\mathrm{\ensuremath{\rho}}^{0}$, the K\ifmmode\bar\else\textasciimacron\fi{} $^{\mathrm{*}0}$ and ${\mathrm{\ensuremath{\rho}}}^{0}$ are found to be polarized with their spins oriented in the direction of their motion as seen from the ${\mathit{D}}^{0}$ frame.