Absolute measurements of branching fractions of Cabibbo-suppressed hadronic $D^{0(+)}$ decays involving multiple pions

By analyzing $e^{+}{e}^{-}$ annihilation data with an integrated luminosity of $2.93{\mathrm{fb}}^{-1}$ collected at the center-of-mass energy $\sqrt{s}=3.773\mathrm{GeV}$ with the BESIII detector, we present the first absolute measurements of the branching fractions of twenty Cabibbo-suppressed hadronic $D^{0(+)}$ decays involving multiple pions. The highest four branching fractions obtained are $\mathcal{B}(D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0)=(1.343\pm 0.013_{\mathrm{stat}}\pm 0.016_{\mathrm{syst}})\%$, $\mathcal{B}(D^0\to {\pi }^{+}{\pi }^{-}2{\pi }^0)=(1.002\pm 0.019_{\mathrm{stat}}\pm 0.024_{\mathrm{syst}})\%$, $\mathcal{B}(D^{+}\to 2{\pi }^{+}{\pi }^{-}{\pi }^0)=(1.165\pm 0.021_{\mathrm{stat}}\pm 0.021_{\mathrm{syst}})\%$, and $\mathcal{B}(D^{+}\to 2{\pi }^{+}{\pi }^{-}2{\pi }^0)=(1.074\pm 0.040_{\mathrm{stat}}\pm 0.030_{\mathrm{syst}})\%$. The $CP$ asymmetries for the six decays with highest signal yields are also determined and found to be compatible with zero.

Figure 1

The $M_{\mathrm{BC}}^{\mathrm{tag}}$ versus $M_{\mathrm{BC}}^{\mathrm{sig}}$ distribution of the accepted DT candidates of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ in data. Here, the ISR denotes initial state radiation, which spreads along the diagonal direction and extends to the higher $M_{\mathrm{BC}}$ side. The $D_{\text{right}}^{\mathrm{sig}}$ and $D_{\text{right}}^{\mathrm{tag}}$ denote the signal spreading around $M_{\mathrm{BC}}^{\mathrm{sig}}=M_D$ and $M_{\mathrm{BC}}^{\mathrm{tag}}=M_D$.

Figure 2

Projections of $M_{\mathrm{BC}}^{\mathrm{tag}}$ (left) and $M_{\mathrm{BC}}^{\mathrm{sig}}$ (right) of the 2D fits to the DT candidate events. Points with error bars are data and blue solid curves are the fit results. Black dotted, cyan blue solid, blue dotted, red dotted, and pink long-dashed correspond to the fitted signal, fixed peaking background, BKGI, BKGII, and BKGIII components, respectively.

Figure 3

Comparisons of the distributions of invariant masses of two-body particle combinations, momenta and $\cos \theta$ of daughter particles for the $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ candidates between data (points with error bars) and the BODY3 signal MC events (black solid line histograms) plus the MC-simulated backgrounds from the inclusive MC sample (yellow filled histograms).