Observation of ${h}_{1}\left(1380\right)$ in the $J/\psi \to {\eta }^{\prime }K\overline{K}\pi $ decay

Using $1.31×{10}^{9}\text{}\text{}J/\psi $ events collected by the BESIII detector at the BEPCII ${e}^{+}{e}^{-}$ collider, we report the first observation of the ${h}_{1}\left(1380\right)$ in $J/\psi \to {\eta }^{\prime }{h}_{1}\left(1380\right)$ with a significance of more than ten standard deviations. The mass and width of the possible axial-vector strangeonium candidate ${h}_{1}\left(1380\right)$ are measured to be $M=\left(1423.2±2.1±7.3\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\Gamma =\left(90.3±9.8±17.5\right)\text{}\text{}\mathrm{MeV}$. The product branching fractions, assuming no interference, are determined to be $B\left(J/\psi \to {\eta }^{\prime }{h}_{1}\left(1380\right)\right)×B\left({h}_{1}\left(1380\right)\to {K}^{*}\left(892{\right)}^{+}{K}^{-}+c.c.\right)=\left(1.51±0.09±0.21\right)×{10}^{-4}$ in ${\eta }^{\prime }{K}^{+}{K}^{-}{\pi }^{0}$ mode and $B\left(J/\psi \to {\eta }^{\prime }{h}_{1}\left(1380\right)\right)×B\left({h}_{1}\left(1380\right)\to {K}^{*}\left(892\right)\overline{K}+c.c.\right)=\left(2.16±0.12±0.29\right)×{10}^{-4}$ in ${\eta }^{\prime }{K}_{S}^{0}{K}^{±}{\pi }^{\mp }$ mode. The first uncertainties are statistical and the second are systematic. Isospin symmetry violation is observed in the decays ${h}_{1}\left(1380\right)\to {K}^{*}\left(892{\right)}^{+}{K}^{-}+c.c.$ and ${h}_{1}\left(1380\right)\to {K}^{*}\left(892{\right)}^{0}{\overline{K}}^{0}+c.c.$. Based on the measured ${h}_{1}\left(1380\right)$ mass, the mixing angle between the states ${h}_{1}\left(1170\right)$ and ${h}_{1}\left(1380\right)$ is determined to be $\left(35.9±2.6\right)°$, consistent with theoretical expectations.