Observation of the Singly Cabibbo-Suppressed Decay $D^{+}\to\omega\pi^{+}$ and Evidence for $D^{0}\to\omega\pi^{0}$

Based on 2.93 fb$^{-1}$ $e^+e^-$ collision data taken at center-of-mass energy of 3.773 GeV by the BESIII detector, we report searches for the singly Cabibbo-suppressed decays $D^{+}\to\omega\pi^{+}$ and $D^{0}\to\omega\pi^{0}$. A double tag technique is used to measure the absolute branching fractions $\mathcal{B}(D^{+}\to\omega\pi^{+})=(2.79\pm0.57\pm0.16)\times 10^{-4}$ and $\mathcal{B}(D^{0}\to\omega\pi^{0})=(1.17\pm0.34\pm0.07)\times 10^{-4}$, with statistical significances of $5.5\sigma$ and $4.1\sigma$, respectively. We also present measurements of the absolute branching fractions for the related $\eta \pi$ decay modes. We find $\mathcal{B}(D^{+}\to\eta\pi^{+})=(3.07\pm0.22\pm0.13)\times10^{-3}$ and $\mathcal{B}(D^{0}\to\eta\pi^{0})=(0.65\pm0.09\pm0.04)\times10^{-3}$, which are consistent with the current world averages. The first and second uncertainties are statistical and systematic, respectively.