Measurement of singly Cabibbo-suppressed decays → , , And

Using a data sample of ${e}^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 2.93 $\text{fb}{}^{-1}$ collected with the BESIII detector at a center-of-mass energy of $\sqrt{s}=3.773\phantom{\rule{0.25em}{0ex}}\text{GeV}$, we search for the singly Cabibbo-suppressed decays ${D}^{0}\to {\pi }^{0}{\pi }^{0}{\pi }^{0}$, ${\pi }^{0}{\pi }^{0}\eta $, ${\pi }^{0}\eta \eta $ and ηηη using the double tag method. The absolute branching fractions are measured to be $B\left({D}^{0}\to {\pi }^{0}{\pi }^{0}{\pi }^{0}\right)=\left(2.0±0.4±0.3\right)×{10}^{-4}$, $B\left({D}^{0}\to {\pi }^{0}{\pi }^{0}\eta \right)=\left(3.8±1.1±0.7\right)×{10}^{-4}$ and $B\left({D}^{0}\to {\pi }^{0}\eta \eta \right)=\left(7.3±1.6±1.5\right)×{10}^{-4}$ with the statistical significances of 4.8σ, 3.8σ and 5.5σ, respectively, where the first uncertainties are statistical and the second ones systematic. No significant signal of ${D}^{0}\to \eta \eta \eta $ is found, and the upper limit on its decay branching fraction is set to be $B\left({D}^{0}\to \eta \eta \eta \right)<1.3×{10}^{-4}$ at the 90% confidence level.