Observation of $\psi (3686)\to 3\varphi$

Using $(2.712\pm 0.014)\times {10}^9\psi (3686)$ events collected by the BESIII detector operating at the BEPCII collider, we report the first observation of $\psi (3686)\to 3\varphi$ decay with a significance larger than $10\sigma$. The branching fraction of this decay is determined to be $(1.46\pm 0.05\pm 0.17)\times {10}^{-5}$, where the first uncertainty is statistical and the second is systematic. No significant structure is observed in the $\varphi \varphi$ invariant mass spectra.

Figure 1

The $M_{K^{+}{K}^{-}}^a:M_{K^{+}{K}^{-}}^b:M_{K^{+}{K}^{-}}^c(M_{\varphi }^{\mathrm{rec}})$ distributions of the (left) full and (right) partial reconstructed candidates for $\psi (3686)\to 3\varphi$.

Figure 2

Dalitz plots of $M_{{\varphi }^a{\varphi }^b}^2$ vs $M_{{\varphi }^a{\varphi }^c}^2$ of the (left) full and (right) partial reconstructed candidates. The first row indicates data and the second row indicates signal MC events. In the third row, the distributions of the invariant masses of the two lowest momentum $\varphi$ candidates are shown. The black points with error bars are data. The blue curves represent the signal component of the fit.

Figure 3

Distributions of the momentum, cosines of polar angle and mass spectra of the $\varphi$ candidates for full reconstructed candidates, all reconstructed $\varphi$ candidates are filled in the same histogram. The black points with error bars are data, the solid red lines show the signal MC simulation which is scaled to the total number of events of data, and the blue solid-filled histograms are the background contribution of the inclusive MC sample. The bottom panels show the data and MC comparison, where the error bands indicate the MC statistical uncertainty only.

Figure 4

Distributions of the momentum, cosines of polar angle and mass spectra of the $\varphi$ candidates for partial candidates, two reconstructed $\varphi$ candidates are filled in the same histogram (first column). The black points with error bars are data, the solid red lines show the signal MC simulation which is scaled to the total number of events of data, and the blue solid-filled histograms are the background contribution of the inclusive MC sample. The bottom panels show the data and MC comparison, where the error bands indicate the MC statistical uncertainty only.

Figure 5

One-dimensional projections of the simultaneous fit to the $M_{K^{+}{K}^{-}}^a:M_{K^{+}{K}^{-}}^b:M_{K^{+}{K}^{-}}^c(M_{\varphi }^{\mathrm{rec}})$ distribution of the (top row) full and (bottom row) partial reconstructed candidate events of $\psi (3686)\to 3\varphi$ for $\psi (3686)$ data (shown as the dots with error bars). The red solid curves are the total fit results, while the blue curves are the signal contributions of the fit and other curves represent the different background contributions. For each projection, the ${\chi }^2/\mathrm{NDOF}$ are provided, with ${\chi }^2$ being calculated from the difference between the binned data points and the total fit projection, and the NDOF representing the number of bins.

Figure 6

One-dimensional projections of the simultaneous fit to the $M_{K^{+}{K}^{-}}^a:M_{K^{+}{K}^{-}}^b:M_{K^{+}{K}^{-}}^c(M_{\varphi }^{\mathrm{rec}})$ distribution of the (top row) full and (bottom row) partial reconstructed candidate events of $e^{+}{e}^{-}\to 3\varphi$ for data taken at 3.773 GeV (shown as the dots with error bars). The red solid curves are the total fit results, while the blue curves are the signal contributions of the fit and other curves represent the different background contributions. For each projection, the ${\chi }^2/\mathrm{NDOF}$ are given, with ${\chi }^2$ being calculated from the difference between the binned data points and the total fit projection, and the NDOF representing the number of bins.