Amplitude analysis of the isospin-violating decay 𝐽/𝜓 →𝛾⁢𝜂⁢𝜋0

Using $(10087 \pm 44)\times10^{6}$ $J/\psi$ events collected with the BESIII detector, we perform the first amplitude analysis of the process $J/\psi \to \gamma\eta\pi^0$. The decay is dominated by the intermediate processes $J/\psi \to \pi^0b_1(1235)^0 \to \gamma\eta\pi^0$, $J/\psi \to \pi^0\rho(1450)^0 \to \gamma\eta\pi^0$, and $J/\psi \to \eta h_1(1170) \to \gamma\eta\pi^0$. Contributions from $J/\psi \to \gamma a_0(980)^0 \to \gamma\eta\pi^0$, $J/\psi \to \gamma a_2(1320)^0 \to \gamma\eta\pi^0$, and $J/\psi \to \gamma a_2(1700)^0 \to \gamma\eta\pi^0$ are observed with statistical significances exceeding $5\sigma$, constituting the first observation of radiative transitions of the $J/\psi$ to isospin-triplet scalar mesons. The total branching fraction is measured to be $$\mathcal{B}(J/\psi \to \gamma\eta\pi^0) = (25.7 \pm 0.3\,(\mathrm{stat}) \pm 1.5\,(\mathrm{syst})) \times 10^{-6},$$ where the first uncertainty is statistical and the second is systematic. This result is consistent with the previous measurement, with the precision improved by more than a factor of two.