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Using 2.93 fb−1 of 𝑒+𝑒− collision data taken at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first measurements of the absolute branching fractions of 14 hadronic 𝐷0(+) decays to exclusive final states with an 𝜂, e.g., 𝐷0→𝐾−𝜋+𝜂, 𝐾0𝑆𝜋0𝜂, 𝐾+𝐾−𝜂, 𝐾0𝑆𝐾0𝑆𝜂, 𝐾−𝜋+𝜋0𝜂, 𝐾0𝑆𝜋+𝜋−𝜂, 𝐾0𝑆𝜋0𝜋0𝜂, and 𝜋+𝜋−𝜋0𝜂; 𝐷+→𝐾0𝑆𝜋+𝜂, 𝐾0𝑆𝐾+𝜂, 𝐾−𝜋+𝜋+𝜂, 𝐾0𝑆𝜋+𝜋0𝜂, 𝜋+𝜋+𝜋−𝜂, and 𝜋+𝜋0𝜋0𝜂. Among these decays, the 𝐷0→𝐾−𝜋+𝜂 and 𝐷+→𝐾0 𝑆𝜋+𝜂 decays have the largest branching fractions, which are ℬ(𝐷0→𝐾−𝜋+𝜂) = (1.853±0.025stat±0.031syst)% and ℬ(𝐷+→𝐾0𝑆𝜋+𝜂) = (1.309±0.037stat±0.031syst)%, respectively. The charge-parity asymmetries for the six decays with highest event yields are determined, and no statistically significant charge-parity violation is found.
Cross sections of the process 𝑒+𝑒−→𝜋0𝜋0𝐽/𝜓 at center-of-mass energies between 3.808 and 4.600 GeV are measured with high precision by using 12.4 fb−1 of data samples collected with the BESIII detector operating at the BEPCII collider facility. A fit to the measured energy-dependent cross sections confirms the existence of the charmoniumlike state 𝑌(4220). The mass and width of the 𝑌(4220) are determined to be (4220.4±2.4±2.3) MeV/𝑐2 and (46.2±4.7±2.1) MeV, respectively, where the first uncertainties are statistical and the second systematic. The mass and width are consistent with those measured in the process 𝑒+𝑒−→𝜋+𝜋−𝐽/𝜓. The neutral charmonium-like state 𝑍𝑐(3900)0 is observed prominently in the 𝜋0𝐽/𝜓 invariant-mass spectrum, and, for the first time, an amplitude analysis is performed to study its properties. The spin-parity of 𝑍𝑐(3900)0 is determined to be 𝐽𝑃=1+, and the pole position is (3893.1±2.2±3.0)−𝑖(22.2±2.6±7.0) MeV/𝑐2, which is consistent with previous studies of electrically charged 𝑍𝑐(3900)±. In addition, cross sections of 𝑒+𝑒− → 𝜋0𝑍𝑐(3900)0 → 𝜋0𝜋0𝐽/𝜓 are extracted, and the corresponding line shape is found to agree with that of the 𝑌(4220).