Measurement of the branching fraction of $\psi \left(2S\right)\to \gamma {\pi }^{0}$

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