Measurement of singly Cabibbo-suppressed decays D⁰ → π⁰π⁰π⁰, π⁰π⁰η, π⁰ηη and ηηη

Using a data sample of e⁺e⁻ collision data corresponding to an integrated luminosity of 2.93 fb⁻¹ collected with the BESIII detector at a center-of-mass energy of √s = 3.773 GeV, we search for the singly Cabibbo-suppressed decays D⁰ → π⁰π⁰π⁰ , π⁰π⁰η, π⁰ηη and ηηη using the double tag method. The absolute branching fractions are measured to be Β(D⁰ → π⁰π⁰π⁰) = (2.0 ± 0.4 ± 0.3) × 10⁻⁴ , Β(D⁰ → π⁰π⁰η ) = (3.8 ± 1.1 ± 0.7) × 10⁻⁴ and Β(D⁰ → π⁰ηη) = (7.3 ± 1.6 ± 1.5) × 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 D⁰ → ηηη is found, and the upper limit on its decay branching fraction is set to be Β(D⁰ → ηηη ) < 1.3 × 10⁻⁴ at the 90% confidence level.