Study of $J/\psi \to \eta \varphi {\pi }^{+}{\pi }^{-}$ at BESIII

Based on a sample of $2.25\times {10}^{8}J/\psi$ events taken with the BESIII detector at the BEPCII collider, we present the results of a study of the decay $J/\psi \to \eta \varphi {\pi }^{+}{\pi }^{-}$. The $Y(2175)$ resonance is observed in the invariant mass spectrum of $\varphi f_0(980)$ with a statistical significance of greater than $10\sigma$. The corresponding mass and width are determined to be $M=2200\pm 6(\mathrm{stat})\pm 5(\mathrm{syst})\mathrm{MeV}/c^2$ and $\mathrm{\Gamma }=104\pm 15(\mathrm{stat})\pm 15(\mathrm{syst})\mathrm{MeV}$, respectively, and the product branching fraction is measured to be $\mathcal{B}(J/\psi \to \eta Y(2175),Y(2175)\to \varphi f_0(980),f_0(980)\to {\pi }^{+}{\pi }^{-})=(1.20\pm 0.14(\mathrm{stat})\pm 0.37(\mathrm{syst}))\times {10}^{-4}$. The results are consistent within errors with those of previous experiments. We also measure the branching fraction of $J/\psi \to \varphi f_1(1285)$ with $f_1(1285)\to \eta {\pi }^{+}{\pi }^{-}$ and set upper limits on the branching fractions for $J/\psi \to \varphi \eta (1405)/\varphi X(1835)/\varphi X(1870)$ with $\eta (1405)/X(1835)/X(1870)\to \eta {\pi }^{+}{\pi }^{-}$ at the 90% confidence level.

Figure 1

(a) Scatter plot of $M(\gamma \gamma )$ versus $M(K^{+}{K}^{-})$. The boxes with the dotted and solid lines show the $\eta$ and $\varphi$ signal and sideband regions, respectively. (b) The $\gamma \gamma$ invariant mass spectrum for events with the $K^{+}{K}^{-}$ invariant mass in the $\varphi$ signal region. (c) The $K^{+}{K}^{-}$ invariant mass spectrum for events with the $\gamma \gamma$ invariant mass in the $\eta$ signal region. In panels (b) and (c), the dotted arrows show the signal regions and the solid lines show the sideband regions, which are described in the text.

Figure 2

(a) The ${\pi }^{+}{\pi }^{-}$ invariant mass spectrum. The shaded histogram shows the non-$\eta$ background estimated with the $\eta$ sideband region; the dotted and solid arrows denote the $f_0(980)$ signal and sideband regions, respectively. (b) The scatter plot of $M({\pi }^{+}{\pi }^{-})$ versus $M(K^{+}{K}^{-})$. The solid box shows the signal region, and the dotted boxes show the sideband regions of $\varphi$ and $f_0$. (c) The scatter plot of $M(\varphi {\pi }^{+}{\pi }^{-})$ versus $M({\pi }^{+}{\pi }^{-})$. (d) The $\varphi {\pi }^{+}{\pi }^{-}$ invariant mass distribution after imposing the $f_0(980)$ signal mass window requirement. The shaded histogram shows the background distribution estimated with the sideband method described in the text.

Figure 3

Result of the fit to the $\varphi f_0(980)$ invariant mass distribution described in the text. The circular dots with error bars show the distribution in the signal region; the triangular dots with error bars show the backgrounds estimated using sideband regions; the solid curve shows the overall fit projection; the dotted curve shows the fit for the backgrounds; and the dashed curve is for the sum of the direct decay of $J/\psi \to \eta \varphi f_0$ and the backgrounds.

Figure 4

The fit projections to the $\varphi f_0(980)$ invariant mass distribution showing the (a) constructive and (b) destructive solutions. The short-dashed line denotes the signal distribution; the dot-dashed curve shows the fit to the backgrounds estimated by the sidebands; the long-dashed line denotes the direct decay of $J/\psi \to \eta \varphi f_0$; and the dotted line denotes the interference component.

Figure 5

Fit to the $\eta {\pi }^{+}{\pi }^{-}$ invariant mass spectrum. The solid lines show the total fit and the $f_1(1285)$ and $\eta (1405)$ components; the dashed line denotes the non-$\eta$ and non-$\varphi$ background estimated using the $\eta \text{−}\varphi$ sidebands; the dotted curve represents the $J/\psi \to \eta \varphi {\pi }^{+}{\pi }^{-}$ component; the solid histogram indicates the shape of the $X(1835)$ (with arbitrary normalization); and the dash-dotted histogram shows the predicted shape of the $X(1870)$ signal (with arbitrary normalization).