Resonant substructure in K[over ¯]πππ decays of D mesons

We determine the resonant substructure of $D\to \overline{K}\pi \pi \pi$ decays, extracting the relative fractions and phases of the amplitudes contributing to the $K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$, ${\overline{K}}^0{\pi }^{+}{\pi }^{+}{\pi }^{-}$, $K^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$, and ${\overline{K}}^0{\pi }^{+}{\pi }^{-}{\pi }^0$ final states. We find that two-body decay modes account for at least 75% of these decays. We obtain branching ratios for $D\to {\overline{K}a}_1\mathrm{}\left(1260\right)\mathrm{}$, $D\to {\overline{K}}^{*}\rho$, $D\to {\overline{K}}_1{\mathrm{}\left(1270\right)\mathrm{}}_{\pi }$, $D\to {\overline{K}}_1{\mathrm{}\left(1400\right)\mathrm{}}_{\pi }$, and $D^0\to {\overline{K}}^0\omega$ decay modes, as well as for several three- and four-body decay modes. In the case of $D\to {\overline{K}a}_1\mathrm{}\left(1260\right)\mathrm{}$ and $D\to {\overline{K}}^{*}\rho$, we obtain the branching ratios for all three possible isospin combinations, enabling us to extract the isospin-½ and -$\frac{3}{2}$ amplitudes, and their relative phases. We find that the isospin-$\frac{3}{2}$ amplitudes are suppressed relative to the isospin-½ amplitudes. This implies that the widths of the $D^{+}$ modes are suppressed relative to those of the $D^0$, confirming that an understanding of the lifetime difference of the $D^0$ and $D^{+}$ depends on an understanding of two-body hadronic decays. For the $D\to {\overline{K}}^{*}\rho$ decay modes, we obtain detailed information on the polarization of the ${\overline{K}}^{*}$ and $\rho$. This enables us to place constraints on the form factors for $D\to {\overline{K}}^{*}$ and $D\to \rho$ transitions. A comparison of our results on $D\to {\overline{K}}^{*}\rho$ decays with recent results on semileptonic decays allows us to test the factorization hypothesis.