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

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Abstract

We determine the resonant substructure of $D\ensuremath{\rightarrow}\overline{K}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$ decays, extracting the relative fractions and phases of the amplitudes contributing to the ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, and ${\overline{K}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ final states. We find that two-body decay modes account for at least 75% of these decays. We obtain branching ratios for $D\ensuremath{\rightarrow}{\overline{K}a}_{1}(1260)$, $D\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$, $D\ensuremath{\rightarrow}{\overline{K}}_{1}{(1270)}_{\ensuremath{\pi}}$, $D\ensuremath{\rightarrow}{\overline{K}}_{1}{(1400)}_{\ensuremath{\pi}}$, and ${D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}\ensuremath{\omega}$ decay modes, as well as for several three- and four-body decay modes. In the case of $D\ensuremath{\rightarrow}{\overline{K}a}_{1}(1260)$ and $D\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$, we obtain the branching ratios for all three possible isospin combinations, enabling us to extract the isospin-\textonehalf{} and -$\frac{3}{2}$ amplitudes, and their relative phases. We find that the isospin-$\frac{3}{2}$ amplitudes are suppressed relative to the isospin-\textonehalf{} 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 $D\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$ decay modes, we obtain detailed information on the polarization of the ${\overline{K}}^{*}$ and $\ensuremath{\rho}$. This enables us to place constraints on the form factors for $D\ensuremath{\rightarrow}{\overline{K}}^{*}$ and $D\ensuremath{\rightarrow}\ensuremath{\rho}$ transitions. A comparison of our results on $D\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$ decays with recent results on semileptonic decays allows us to test the factorization hypothesis.

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