Observation and study of the decay $J/\psi \to \varphi \eta {\eta }^{\prime }$

We report the observation and study of the decay $J/\psi \to \varphi \eta {\eta }^{\prime }$ using $1.3\times 10^9$ $J/\psi$ events collected with the BESIII detector. Its branching fraction, including all possible intermediate states, is measured to be $(2.32\pm 0.06\pm 0.16)\times {10}^{-4}$. We also report evidence for a structure, denoted as $X$, in the $\varphi {\eta }^{\prime }$ mass spectrum in the $2.0–2.1\mathrm{GeV}/c^2$ region. Using two decay modes of the ${\eta }^{\prime }$ meson ($\gamma {\pi }^{+}{\pi }^{-}$ and $\eta {\pi }^{+}{\pi }^{-}$), a simultaneous fit to the $\varphi {\eta }^{\prime }$ mass spectra is performed. Assuming the quantum numbers of the $X$ to be $J^P=1^{-}$, its significance is found to be $4.4\sigma$, with a mass and width of $(2002.1\pm 27.5\pm 21.4)\mathrm{MeV}/c^2$ and $(129\pm 17\pm 9)\mathrm{MeV}$, respectively, and a product branching fraction $\mathcal{B}(J/\psi \to \eta X)\times \mathcal{B}(X\to \varphi {\eta }^{\prime })=(9.8\pm 1.2\pm 1.7)\times {10}^{-5}$. Alternatively, assuming $J^P=1^{+}$, the significance is $3.8\sigma$, with a mass and width of $(2062.8\pm 13.1\pm 7.2)\mathrm{MeV}/c^2$ and $(177\pm 36\pm 35)\mathrm{MeV}$, respectively, and a product branching fraction $\mathcal{B}(J/\psi \to \eta X)\times \mathcal{B}(X\to \varphi {\eta }^{\prime })=(9.6\pm 1.4\pm 2.0)\times {10}^{-5}$. The angular distribution of $J/\psi \to \eta X$ is studied and the two $J^P$ assumptions of the $X$ cannot be clearly distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.

Figure 1

The $M({\pi }^{+}{\pi }^{-})$ distribution for mode I, where dots with error bars are experimental data, the (blue) solid histogram shows the signal MC simulation, the (violet) dotted histogram shows the background from the $J/\psi \to \eta \varphi f_0(980)$ process, and the arrow represents the mass requirement.

Figure 2

Distributions of $M(\gamma {\pi }^{+}{\pi }^{-})$ versus $M(K^{+}{K}^{-})$ for mode I (a) and $M(\eta {\pi }^{+}{\pi }^{-})$ versus $M(K^{+}{K}^{-})$ for mode II (b), where the (red) solid rectangles show the signal regions; the (blue) dotted and (green) dashed rectangles represent the 2D sidebands.

Figure 3

Dalitz plots for modes I (a) and II (b).

Figure 4

Results of the simultaneous fit with the $1^{-}$ assumption for modes I (a) and II (b). Dots with error bars are experimental data and the (red) solid curves show the fit model. The (blue) dashed curves are the signal component. The (violet) dotted curves show the background from the $J/\psi \to \varphi \eta {\eta }^{\prime }$ PHSP process. The (orange) dot-dashed curves represent the background from the $J/\psi \to \varphi f_0(1500)$, $f_0(1500)\to \eta {\eta }^{\prime }$ process. The (green) long-dashed curves show the $\mathrm{non}\text{−}\varphi$ and/or $\mathrm{non}\text{−}{\eta }^{\prime }$ backgrounds.

Figure 5

Results of the simultaneous fit with the $1^{+}$ assumption for modes I (a) and II (b). Dots with error bars are experimental data and the (red) solid curves show the fit model. The (blue) dashed curves are the signal component. The (violet) dotted curves show the background from the $J/\psi \to \varphi \eta {\eta }^{\prime }$ PHSP process. The (orange) dot-dashed curves represent the background from the $J/\psi \to \varphi f_0(1500)$, $f_0(1500)\to \eta {\eta }^{\prime }$ process. The (green) long-dashed curves show the $\mathrm{non}\text{−}\varphi$ and/or $\mathrm{non}\text{−}{\eta }^{\prime }$ backgrounds.

Figure 6

Distribution of the $\eta$ polar angle in the $J/\psi$ rest frame. Dots with error bars are experimental data. The (violet) dashed curve is the fitting result with the $1^{-}$ assumption, and the (red) solid curve is that with the $1^{+}$ assumption.