Measurement of the Branching Fraction of \boldmath{$ψ(2S) \to γπ^0$}
Based on $(2712.4\pm14.1)\times10^{6}~ψ(2S)$ events, 7.9 fb$^{-1}$ $ψ(3773)$ data, and 0.8 fb$^{-1}$ off-resonance data samples collected with the BESIII detector, we measure the branching fraction of $ψ(2S)\rightarrowγπ^{0}$ and $e^{+}e^{-}\rightarrowγπ^{0}$ form factor at momentum transfers $Q^{2}\sim13$ GeV$^{2}$. The $e^{+}e^{-}\rightarrowγπ^{0}$ cross section is fitted with considering the interference between the $ψ(2S)$ and continuum amplitudes and two solutions are found, ${\cal B}=3.74\times10^{-7}$ with $ϕ=3.93$ rad and ${\cal B}=7.87\times10^{-7}$ with $ϕ=2.08$ rad. Here, ${\cal B}$ is the branching fraction of $ψ(2S)\rightarrowγπ^{0}$ and $ϕ$ is the relative phase angle between the $ψ(2S)$ and continuum amplitudes. Due to insufficient off-resonance data, the branching fraction ${\cal B}(ψ(2S)\rightarrowγπ^{0})$ is determined to be in the range $[2.7, 9.7]\times10^{-7}$ within one standard deviation of the contour region.