Observation of the doubly Cabibbo-suppressed decays D+→ K+π0π0 and D+→ K+π0η.

By analyzing e⁺e⁻ annihilation data corresponding to an integrated luminosity of 2.93 fb⁻¹ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first observations of the doubly Cabibbo-suppressed decays D⁺→ K⁺π⁰π⁰ and D⁺→ K⁺π⁰η. The branching fractions of D⁺→ K⁺π⁰π⁰ and D⁺→ K⁺π⁰η are measured to be (2.1 ± 0.4_stat ± 0.1_syst) × 10⁻⁴ and (2.1 ± 0.5_stat ± 0.1_syst) × 10⁻⁴ with statistical significances of 8.8σ and 5.5σ, respectively. In addition, we search for the subprocesses D⁺→ K^*(892)⁺π⁰ and D⁺→ K^*(892)⁺η with K^*(892)⁺→ K⁺π⁰. The branching fraction of D⁺→ K^*(892)⁺η is determined to be ( 4.4 − 1.5 stat + 1.8 ± 0.2_syst) × 10⁻⁴, with a statistical significance of 3.2σ. No significant signal for D⁺→ K^*(892)⁺π⁰ is found and we set an upper limit on the branching fraction of this decay at the 90% confidence level to be 5.4 × 10⁻⁴. [ABSTRACT FROM AUTHOR]