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 $2.93~\rm fb^{-1}$ collected at the center-of-mass energy $\sqrt s=$ 3.773 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 largest four branching fractions obtained are $\mathcal{B}(D^0\toπ^+π^-π^0)= (1.343\pm0.013_{\rm stat}\pm0.016_{\rm syst})\%$, $\mathcal{B}(D^0\toπ^+π^-2π^0)= (0.998\pm0.019_{\rm stat}\pm0.024_{\rm syst})\%$, $\mathcal{B}(D^+\to 2π^+π^-π^0)= (1.174\pm0.021_{\rm stat}\pm0.021_{\rm syst})\%$, and $\mathcal{B}(D^+\to 2π^+π^-2π^0)=(1.074\pm0.040_{\rm stat}\pm0.030_{\rm syst})\%$. The $CP$ asymmetries for the six decays with highest event yields are also determined.