Observation of an Isoscalar Resonance with Exotic $J^{PC}=1^{-+}$ Quantum Numbers in $J/\psi \to \gamma \eta {\eta }^{\prime }$

Using a sample of $(10.09\pm 0.04)\times {10}^{9}J/\psi$ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay $J/\psi \to \gamma \eta {\eta }^{\prime }$ is performed. The first observation of an isoscalar state with exotic quantum numbers $J^{PC}=1^{-+}$, denoted as ${\eta }_1(1855)$, is reported in the process $J/\psi \to \gamma {\eta }_1(1855)$ with ${\eta }_1(1855)\to \eta {\eta }^{\prime }$. Its mass and width are measured to be $(1855\pm 9_{-1}^{+6})\mathrm{MeV}/c^2$ and $(188\pm {18}_{-8}^{+3})\mathrm{MeV}$, respectively, where the first uncertainties are statistical and the second are systematic, and its statistical significance is estimated to be larger than $19\sigma$.

Figure 1

Background-subtracted data (black points) and the PWA fit projections (lines) for (a),(b),(c) the invariant mass distributions of (a) $\eta {\eta }^{\prime }$, (b) $\gamma \eta$, and (c) $\gamma {\eta }^{\prime }$, and (d),(e) the distribution of $\cos {\theta }_{\eta }$, where ${\theta }_{\eta }$ is the angle of the $\eta$ momentum in the $\eta {\eta }^{\prime }$ (Jocob and Wick) helicity frame for (d) all $\eta {\eta }^{\prime }$ masses and (e) $\eta {\eta }^{\prime }$ masses between 1.7 and $2.0\mathrm{GeV}/c^2$. The red lines are the total fit projections from the baseline PWA. The blue lines are the total fit projections from a fit excluding the ${\eta }_1$ component. The dashed lines for the $1^{-+},0^{++},2^{++},4^{++}$, and $1^{+-}$ contributions are the coherent sums of amplitudes for each $J^{PC}$. Note that the process $J/\psi \to \varphi {\eta }^{\prime }$, $\varphi \to \gamma \eta$ is rejected, which leads to the depletion of events around $1.02\mathrm{GeV}/c^2$ in $\mathrm{M}(\gamma \eta )$.

Figure 2

Dalitz plots for (a) the baseline PWA, (b) the selected data, and (c) background estimated from the ${\eta }^{\prime }$ sideband. Note that the process $J/\psi \to \varphi {\eta }^{\prime }$, $\varphi \to \gamma \eta$ is rejected, which leads to the depletion of events in a band around $1{\mathrm{GeV}}^2/c^4$ in ${\mathrm{M}}^2(\gamma \eta )$.

Figure 3

The distributions of the unnormalized moments $⟨Y_L^0⟩$ ($L=0$, 1, 2, and 4) for $J/\psi \to \gamma \eta {\eta }^{\prime }$ as functions of the $\eta {\eta }^{\prime }$ mass. Black dots with error bars represent the background-subtracted data weighted with angular moments; the red solid lines represent the baseline fit projections; and the blue dotted lines represent the projections from a fit excluding the ${\eta }_1$ component.