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Based on a sample of 1.31 × 10 9 J=ψ events collected with the BESIII detector, the matrix elements for the decays η 0 → ηπ þ π − and η 0 → ηπ 0 π 0 are determined using 351,016 η 0 → ðη → γγÞπ þ π − and 56,249 η 0 → ðη → γγÞπ 0 π 0 events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between η 0 → ηπ þ π − and η 0 → ηπ 0 π 0 is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in η 0 → ηπ 0 π 0 is observed.

We report the first observation of a_{0}^{0}(980)-f_{0}(980) mixing in the decays of J/ψ→ϕf_{0}(980)→ϕa_{0}^{0}(980)→ϕηπ^{0} and χ_{c1}→a_{0}^{0}(980)π^{0}→f_{0}(980)π^{0}→π^{+}π^{-}π^{0}, using data samples of 1.31×10^{9}  J/ψ events and 4.48×10^{8}  ψ(3686) events accumulated with the BESIII detector. The signals of f_{0}(980)→a_{0}^{0}(980) and a_{0}^{0}(980)→f_{0}(980) mixing are observed at levels of statistical significance of 7.4σ and 5.5σ, respectively. The corresponding branching fractions and mixing intensities are measured and the constraint regions on the coupling constants, g_{a_{0}K^{+}K^{-}} and g_{f_{0}K^{+}K^{-}}, are estimated. The results improve the understanding of the nature of a_{0}^{0}(980) and f_{0}(980).

By analyzing 482 pb −1 of e þ e − collision data collected at the center-of-mass energy ffiffi ffi s p ¼ 4.009 GeV with the BESIII detector, we measure the branching fractions for the semi-leptonic decays.06 AE 0.54 AE 0.07Þ%, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions for the three semi-muonic decays D þ s → ϕμ þ ν μ ; ημ þ ν μ and η 0 μ þ ν μ are determined for the first time and that of D þ s → ϕe þ ν e is consistent with the world average value within uncertainties.

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