Measurement of the Branching Fraction of \boldmath{$\psi (2S)\to \gamma {\pi }^0$}

Based on $(2712.4\pm 14.1)\times {10}^6\psi (2S)$ events, 7.9 fb${}^{-1}$ $\psi (3773)$ data, and 0.8 fb${}^{-1}$ off-resonance data samples collected with the BESIII detector, we measure the branching fraction of $\psi (2S)\to \gamma {\pi }^0$ and $e^{+}{e}^{-}\to \gamma {\pi }^0$ form factor at momentum transfers $Q^2\sim 13$ GeV${}^2$. The $e^{+}{e}^{-}\to \gamma {\pi }^0$ cross section is fitted with considering the interference between the $\psi (2S)$ and continuum amplitudes and two solutions are found, $\mathcal{B}=3.74\times {10}^{-7}$ with $\phi =3.93$ rad and $\mathcal{B}=7.87\times {10}^{-7}$ with $\phi =2.08$ rad. Here, $\mathcal{B}$ is the branching fraction of $\psi (2S)\to \gamma {\pi }^0$ and $\phi$ is the relative phase angle between the $\psi (2S)$ and continuum amplitudes. Due to insufficient off-resonance data, the branching fraction $\mathcal{B}(\psi (2S)\to \gamma {\pi }^0)$ is determined to be in the range $[2.7,9.7]\times {10}^{-7}$ within one standard deviation of the contour region.