Observation of D+ → ηηπ+ and improved measurement of D0(+) → ηπ+π−(0)

Using an e+e− annihilation data sample 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 measure the absolute branching fractions of D+ → ηηπ+, D+ → ηπ+π0, and D0 → ηπ+π− to be (2.96 ± 0.24 ± 0.10) × 10−3, (2.23 ± 0.15 ± 0.10) × 10−3, and (1.20 ± 0.07 ± 0.04) × 10−3, respectively, where the first uncertainties are statistical and the second ones are systematic. The D+ → ηηπ+ decay is observed for the first time, and the branching fractions of D+(0) → ηπ+π0 (−) are measured with much improved precision. In addition we test for CP asymmetries in the separated charge-conjugate branching fractions; no evidence of CP violation is found.