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

By analyzing ${e}^{+}{e}^{-}$ annihilation data with an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ collected at the center-of-mass energy $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$ with the BESIII detector, we present the first absolute measurements of the branching fractions of twenty Cabibbo-suppressed hadronic ${D}^{0\left(+\right)}$ decays involving multiple pions. The highest four branching fractions obtained are $B\left({D}^{0}\to {\pi }^{+}{\pi }^{-}{\pi }^{0}\right)=\left(1.343±0.01{3}_{\mathrm{stat}}±0.01{6}_{\mathrm{syst}}\right)%$, $B\left({D}^{0}\to {\pi }^{+}{\pi }^{-}2{\pi }^{0}\right)=\left(1.002±0.01{9}_{\mathrm{stat}}±0.02{4}_{\mathrm{syst}}\right)%$, $B\left({D}^{+}\to 2{\pi }^{+}{\pi }^{-}{\pi }^{0}\right)=\left(1.165±0.02{1}_{\mathrm{stat}}±0.02{1}_{\mathrm{syst}}\right)%$, and $B\left({D}^{+}\to 2{\pi }^{+}{\pi }^{-}2{\pi }^{0}\right)=\left(1.074±0.04{0}_{\mathrm{stat}}±0.03{0}_{\mathrm{syst}}\right)%$. The $CP$ asymmetries for the six decays with highest signal yields are also determined and found to be compatible with zero.