Precise branching ratio measurements of the decays $D^0\to {\pi }^{-}{\pi }^{+}{\pi }^0$ and $D^0\to K^{-}{K}^{+}{\pi }^0$ relative to the $D^0\to K^{-}{\pi }^{+}{\pi }^0$ decay

Using $232{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data recorded by the BABAR experiment, we measure the rates of three-body Cabibbo-suppressed decays of the $D^0$ meson relative to the Cabibbo-favored decay, $D^0\to K^{-}{\pi }^{+}{\pi }^0$. We find: $\frac{B(D^0\to {\pi }^{-}{\pi }^{+}{\pi }^0)}{B(D^0\to K^{-}{\pi }^{+}{\pi }^0)}=(10.59\pm 0.06\pm 0.13)\times {10}^{-2}$ and $\frac{B(D^0\to K^{-}{K}^{+}{\pi }^0)}{B(D^0\to K^{-}{\pi }^{+}{\pi }^0)}=(2.37\pm 0.03\pm 0.04)\times {10}^{-2}$, where the errors are statistical and systematic, respectively. These measurements are significantly more precise than the current world average measurements.

Figure 1

Simulated ${\pi }^{-}{\pi }^{+}{\pi }^0$ (top) and $K^{-}{K}^{+}{\pi }^0$ (bottom) invariant mass distributions. Signal events are shown as open histograms. Combinatorial and reflection backgrounds are shown by the light and dark shaded histograms, respectively. The signal region is delimited by the vertical lines.

Figure 2

Fitted mass for the $K^{-}{\pi }^{+}{\pi }^0$, ${\pi }^{-}{\pi }^{+}{\pi }^0$, and $K^{-}{K}^{+}{\pi }^0$ data samples. Dots are data points and the solid curves are the fit. The dot-dashed lines show the level of combinatorial background in each case. For the ${\pi }^{-}{\pi }^{+}{\pi }^0$ and the $K^{-}{K}^{+}{\pi }^0$ modes, the shaded region represents the total background.