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Measurement of the branching fractions for $J/ψ\toγπ^0$, $γη$ and $γη^{\prime}$

The decay modes $\jpsi\arγπ^0, γη$ and $γ\etap$ are analyzed using a data sample of 58 million $\jpsi$ decays collected with the BESII detector at BEPC. The branching fractions are determined to be: $Br(\jpsi\arγπ^0)=(3.13^{+0.65}_{-0.44})\times10^{-5}$, $Br(\jpsi\arγη)=(11.23\pm0.89)\times10^{-4}$, and $Br(\jpsi\arγ\etap)=(5.55\pm0.44)\times10^{-3}$, where the errors are combined statistical and systematic errors. The ratio of partial widths $Γ(\jpsi\arγ\etap)/Γ(\jpsi\arγη)$ is measured to be $4.94\pm0.40$, and the singlet-octet pseudoscalar mixing angle of $η-\etap$ system is determined to be $θ_{P}=(-22.08\pm0.81)^{\circ}$.