Measurement of singly Cabibbo-suppressed decays $D\to \omega \pi \pi$

Using $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at a center-of-mass energy of 3.773 GeV by the BESIII detector at the BEPCII, we measure the branching fractions of the singly Cabibbo-suppressed decays $D\to \omega \pi \pi$ to be $\mathcal{B}(D^0\to \omega {\pi }^{+}{\pi }^{-})=(1.33\pm 0.16\pm 0.12)\times {10}^{-3}$ and $\mathcal{B}(D^{+}\to \omega {\pi }^{+}{\pi }^0)=(3.87\pm 0.83\pm 0.25)\times {10}^{-3}$, where the first uncertainties are statistical and the second ones systematic. The statistical significances are $12.9\sigma$ and $7.7\sigma$, respectively. The precision of $\mathcal{B}(D^0\to \omega {\pi }^{+}{\pi }^{-})$ is improved by a factor of 2.1 over prior measurements, and $\mathcal{B}(D^{+}\to \omega {\pi }^{+}{\pi }^0)$ is measured for the first time. No significant signal for $D^0\to \omega {\pi }^0{\pi }^0$ is observed, and the upper limit on the branching fraction is $\mathcal{B}(D^0\to \omega {\pi }^0{\pi }^0)<1.10\times {10}^{-3}$ at the 90% confidence level. The branching fractions of $D\to \eta \pi \pi$ are also measured and consistent with existing results.

Figure 1

Fits to the $M_{\mathrm{BC}}^{\mathrm{tag}}$ distributions for the ST modes: (a) ${\overline{D}}^0\to K^{+}{\pi }^{-}$, (b) ${\overline{D}}^0\to K^{+}{\pi }^{-}{\pi }^0$, (c) ${\overline{D}}^0\to K^{+}{\pi }^{-}{\pi }^{-}{\pi }^{+}$, (d) $D^{-}\to K^{+}{\pi }^{-}{\pi }^{-}$, (e) $D^{-}\to K^{+}{\pi }^{-}{\pi }^{-}{\pi }^0$, (f) $D^{-}\to K_S^0{\pi }^{-}$, (g) $D^{-}\to K_S^0{\pi }^{-}{\pi }^0$, (h) $D^{-}\to K_S^0{\pi }^{-}{\pi }^{-}{\pi }^{+}$, and (i) $D^{-}\to K^{+}{K}^{-}{\pi }^{-}$. Black dots with error bars represent data, green dashed-dot curves are the combinatorial background, red dashed curves are the signal shape, and the blue solid curves are the total fit curves.

Figure 2

Fits to the $M_{{\pi }^{+}{\pi }^{-}{\pi }^0}$ distributions for the processes: (a) $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^{+}{\pi }^{-}$, (b) $D^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^{+}{\pi }^0$, and (c) $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0{\pi }^0$, together with the background predictions from various MC samples shown by the histograms with diagonal pattern lines. The MC samples of $\psi (3770)\to D\overline{D}$ decays include various background processes only. Black dots with error bars are data, dashed red curves are combinatorial background, dotted cyan and green curves are $\eta$ and $\omega$ signals, and the solid blue curves are the total fit curves. The two green and cyan arrow lines represent the $\omega$ and $\eta$ signal regions, respectively, and the two red arrows represent their low- and high-sideband regions.

Figure 3

The 2D distributions of $M_{\mathrm{BC}}^{\mathrm{tag}}$ versus $M_{\mathrm{BC}}^{\mathrm{sig}}$ for the DT candidate events of $\psi (3770)\to D^0\overline{D^0}$ (top) and $D^{+}{D}^{-}$ (bottom).

Figure 4

Projection plots of the 2D fit to the distribution of $M_{\mathrm{BC}}^{\mathrm{tag}}$ versus $M_{\mathrm{BC}}^{\mathrm{sig}}$ for the DT candidate events in (top) $\omega$ and (bottom) $\eta$ signal regions. Black dots with error bars are data, the solid blue, dashed green, dotted cyan and dashed-dotted red, long dashed-dotted pink, and long dashed brown curves represent the overall fit results, signal, BKGI, BKGII, and BKGIII, respectively. In each panel, the top plot is for $M_{\mathrm{BC}}^{\mathrm{sig}}$ and bottom for $M_{\mathrm{BC}}^{\mathrm{tag}}$.

Figure 5

Projection plots of the 2D fit to the distribution of $M_{\mathrm{BC}}^{\mathrm{tag}}$ versus $M_{\mathrm{BC}}^{\mathrm{sig}}$ for the DT candidate events in (top) $\omega$ and (bottom) $\eta$ sideband regions. Black dots with error bars are data, the solid blue, dashed green, dotted cyan and dashed-dotted red, long dashed-dotted pink, and long dashed brown curves are the overall fit results, signal, BKGI, BKGII, and BKGIII, respectively. In each panel, the top plot is for $M_{\mathrm{BC}}^{\mathrm{sig}}$ and bottom for $M_{\mathrm{BC}}^{\mathrm{tag}}$.