$\eta {\pi }^{+}{\pi }^{-}$ Resonant Structure around $1.8\mathrm{GeV}/c^2$ and $\eta (1405)$ in $J/\psi \to \omega \eta {\pi }^{+}{\pi }^{-}$

We present results of a study of the decay $J/\psi \to \omega \eta {\pi }^{+}{\pi }^{-}$ using a sample of $(225.2\pm 2.8)\times {10}^6$ $J/\psi$ events collected by the BESIII detector, and report the observation of a new process $J/\psi \to \omega X(1870)$ with a statistical significance of $7.2\sigma$, in which $X(1870)$ decays to $a_0^{\pm }(980){\pi }^{\mp }$. Fitting to $\eta {\pi }^{+}{\pi }^{-}$ mass spectrum yields a mass $M=1877.3\pm 6.3(\mathrm{stat}{)}_{-7.4}^{+3.4}(\mathrm{syst})\mathrm{MeV}/c^2$, a width $\Gamma =57\pm 12(\mathrm{stat}{)}_{-4}^{+19}(\mathrm{syst})\mathrm{MeV}/c^2$, and a product branching fraction $\mathcal{B}(J/\psi \to \omega X)\times \mathcal{B}\mathbf{(}X\to a_0^{\pm }(980){\pi }^{\mp }\mathbf{)}\times \mathcal{B}\mathbf{(}{a}_0^{\pm }(980)\to \eta {\pi }^{\pm }\mathbf{)}=[1.50\pm 0.26(\mathrm{stat}{)}_{-0.36}^{+0.72}(\mathrm{syst})]\times {10}^{-4}$. Signals for $J/\psi \to \omega f_1(1285)$ and $J/\psi \to \omega \eta (1405)$ are also clearly observed and measured.

Figure 1

Scatter plot of $M_{\eta (\gamma \gamma )}$ versus $M_{\omega ({\pi }^{+}{\pi }^{-}{\pi }^0)}$. The rectangle in the middle shows the signal region defined as $|M_{{\pi }^{+}{\pi }^{-}{\pi }^0}-m_{\omega }|<28\mathrm{MeV}/c^2$ and $|M_{\gamma \gamma }-m_{\eta }|<24\mathrm{MeV}/c^2$.

Figure 2

Invariant-mass distributions for the selected events: (a) and (b) are the invariant-mass spectra of $\eta {\pi }^{+}{\pi }^{-}$ and $\eta {\pi }^{\pm }$ after the application of all the event-selection criteria; (c) is the $\eta {\pi }^{+}{\pi }^{-}$ mass spectrum for events with an $a_0(980)$ in the $\eta {\pi }^{\pm }$ final state; (d) is the $\eta {\pi }^{+}{\pi }^{-}$ invariant-mass distribution for events with no $a_0(980)$ in the $\eta {\pi }^{\pm }$ system. The histograms in (a) and (c) are the phase-space MC events of $J/\psi \to \omega \eta {\pi }^{+}{\pi }^{-}$ after the same event selection and with arbitrary normalization.

Figure 3

Definition of the signal and two-dimensional side bands.

Figure 4

Results of the fit to the $M(\eta {\pi }^{+}{\pi }^{-})$ mass distribution for events with either the $\eta {\pi }^{+}$ or $\eta {\pi }^{-}$ in the $a_0(980)$ mass window. The dotted curve shows the contribution of non-$\omega$ and/or non-$a_0(980)$ background, the dashed line also includes the contribution from $J/\psi \to b_1(1235)a_0(980)$, and the dot-dashed curve indicates the total background with the nonresonant $J/\psi \to \omega a_0^{\pm }(980){\pi }^{\mp }$ included. ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ is 1.27 for this fit.