Study of $a_0^0(980)-f_0(980)$ mixing

Using samples of $2.25\times {10}^8$ $J/\psi$ events and $1.06\times {10}^8$ ${\psi }^{\prime }$ events collected with the BES III detector, we study the $f_0(980)\to a_0^0(980)$ and $a_0^0(980)\to f_0(980)$ transitions in the processes $J/\psi \to \varphi f_0(980)\to \varphi a_0^0(980)$ and ${\chi }_{c1}\to {\pi }^0{a}_0^0(980)\to {\pi }^0{f}_0(980)$, respectively. Evidence for $f_0(980)\to a_0^0(980)$ is found with a significance of $3.4\sigma$, while in the case of $a_0^0(980)\to f_0(980)$ transition, the significance is $1.9\sigma$. Measurements and upper limits of both branching ratios and mixing intensities are determined.

Figure 1

(a) The invariant mass spectrum of $K^{+}{K}^{-}$ in $J/\psi \to K^{+}{K}^{-}\eta {\pi }^0$. The solid arrows show the $\varphi$ mass window. The dashed arrows show the $\varphi$ sideband region used to estimate backgrounds. The $\eta {\pi }^0$ invariant mass of selected events is shown in (b)–(d). The dots with error bars show the mass spectrum of $M_{\eta {\pi }^0}$ recoiling against the $\varphi$. The shaded histogram is (b) recoiling against the $\varphi$ sideband; (c) from exclusive MC; and (d) from inclusive MC.

Figure 2

Results of the simultaneous fit of the $\eta {\pi }^0$ mass spectra: (a) recoiling against the $\varphi$ and (b) recoiling against the $\varphi$ sideband. The solid curve in the result of the fit described in the text. The dotted curve is the mixing signal, and the dash-dotted curve is the $a_0^0(980)$ contribution from ${\gamma }^{*}$ or $K^{*}K$ loops. The dashed curves in (a) and (b) denote the background polynomial.

Figure 3

(a) The invariant mass spectrum of ${\pi }^0{\pi }^{+}{\pi }^{-}$ in ${\psi }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}{\pi }^0$. The solid arrows show the ${\chi }_{c1}$ mass window, and the dashed arrows show the ${\chi }_{c1}$ sideband region used to estimate background. The invariant mass of ${\pi }^{+}{\pi }^{-}$ of selected events is shown in (b)–(d). The dots with error bars show the mass spectrum of $M_{{\pi }^{+}{\pi }^{-}}$ in the ${\chi }_{c1}$ mass window. The shaded histogram is (b) ${\chi }_{c1}$ sideband; (c) from exclusive MC; and (d) from inclusive MC.

Figure 4

Results of the simultaneous fit of the ${\pi }^{+}{\pi }^{-}$ mass spectra: (a) in the ${\chi }_{c1}$ mass window and (b) in the ${\chi }_{c1}$ sideband region. The solid curve is the result of fit described in the text. The dotted curve shows the mixing signal. The dash-dotted curve indicates $f_0(980)$ from other processes. The dashed curves in (a) and (b) denote the background polynomial.

Figure 5

Mixing intensities of $f_0(980)\to a_0^0(980)$ and $a_0^0(980)\to f_0(980)$. The dots are predictions for the mixing intensities with theoretical and experimental values of the parameters [14]. The shaded region is our results with statistical errors and systematics due to this measurement and the parameterization. The solid lines mark the upper limits.