Measurement of the branching fractions of doubly Cabibbo-suppressed $\textit{D}$ decays

By analyzing $\textit{e}$ $\textit{e}$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, corresponding to an integrated luminosity of 20.3 fb , we measure the branching fractions of the doubly Cabibbo-suppressed (DCS) decays $\textit{D}$ $\textit{→ K}$ $\textit{π}$ , $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ $\textit{π}$ , $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ , $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ $\textit{π}$ , $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ , and $\textit{D}$ $\textit{→ K}$ $\textit{K}$ $\textit{K}$ . We also perform the first searches for $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{η}$, $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ $\textit{η}$, $\textit{D}$ $\textit{→ K}$ $\textit{π}$ $\textit{π}$ $\textit{η}$, $\textit{D}$ → $\textit{K}$ ($\textit{π}$ $\textit{π}$ $\textit{η}$) , and $\textit{D}$ → $\textit{K}$ $\textit{ηη}$ and report the first observations and evidence for some of these final states. Combining the measurements with the world averages of the corresponding Cabibbo-favored (CF) decays, the ratios of the DCS/CF branching fractions are obtained. For the $\textit{D}$ → $\textit{K}$ ($\textit{π}$ $\textit{π}$ $\textit{η}$) decay, the ratio is significantly larger than the corresponding ratios of the other DCS decays.