Study of the decay $J/ψ\to φπ^{0}η$

Based on $(10.09 \pm 0.04) \times 10^9$ $J/ψ$ events collected with the BESIII detector operating at the BEPCII collider, a partial wave analysis of the decay $J/ψ\to φπ^{0}η$ is performed. We observe for the first time two new structures on the $φη$ invariant mass distribution, with statistical significances of $24.0σ$ and $16.9σ$; the first with $J^{\rm PC}$ = $1^{+-}$, mass M = (1911 $\pm$ 6 (stat.) $\pm$ 14 (sys.))~MeV/$c^{2}$, and width $Γ= $ (149 $\pm$ 12 (stat.) $\pm$ 23 (sys.))~MeV, the second with $J^{\rm PC}$ = $1^{--}$, mass M = (1996 $\pm$ 11 (stat.) $\pm$ 30 (sys.))~MeV/$c^{2}$, and width $Γ$ = (148 $\pm$ 16 (stat.) $\pm$ 66 (sys.))~MeV. These measurements provide important input for the strangeonium spectrum. In addition, the $f_0(980)-a_0(980)^0$ mixing signal in $J/ψ\to φf_0(980) \to φa_0(980)^0$ and the corresponding electromagnetic decay $J/ψ\to φa_0(980)^0$ are measured with improved precision, providing crucial information to understand the nature of $a_0(980)^0$ and $f_0(980)$.