Observation of an Anomalous Line Shape of the ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ Mass Spectrum near the $p\overline{p}$ Mass Threshold in $J/\psi \to \gamma {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$

Using $1.09\times {10}^9$ $J/\psi$ events collected by the BESIII experiment in 2012, we study the $J/\psi \to \gamma {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ process and observe a significant abrupt change in the slope of the ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ invariant mass distribution at the proton-antiproton ($p\overline{p}$) mass threshold. We use two models to characterize the ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ line shape around $1.85\mathrm{GeV}/c^2$: one that explicitly incorporates the opening of a decay threshold in the mass spectrum (Flatté formula), and another that is the coherent sum of two resonant amplitudes. Both fits show almost equally good agreement with data, and suggest the existence of either a broad state around $1.85\mathrm{GeV}/c^2$ with strong couplings to the $p\overline{p}$ final states or a narrow state just below the $p\overline{p}$ mass threshold. Although we cannot distinguish between the fits, either one supports the existence of a $p\overline{p}$ moleculelike state or bound state with greater than $7\sigma$ significance.

Figure 1

The ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ invariant mass spectra after the application of all selection criteria. The plot on the left side shows the spectrum for events with the ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$ channel, and that on the right shows the spectrum for the ${\eta }^{\prime }\to \eta (\to \gamma \gamma ){\pi }^{+}{\pi }^{-}$ channel. In both plots, the dots with error bars are data, the shaded histograms are the background, the solid histograms are phase space (PHSP) MC events of $J/\psi \to \gamma {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ (arbitrary normalization), and the dotted vertical line shows the position of the $p\overline{p}$ mass threshold.

Figure 2

Fit results with simple Breit-Wigner formulas. The dashed dotted vertical line shows the position of the $p\overline{p}$ mass threshold, the dots with error bars are data, the solid curves are total fit results, the dashed curves are the $X(1835)$, the short-dashed curves are the $f_1(1510)$, the dash-dot curves are the $X(2120)$, and the long-dashed curves are the nonresonant ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ fit results; the shaded histograms are background events. The inset shows the data and the global fit between 1.8 and $1.95\mathrm{GeV}/c^2$.

Figure 3

Fit results of using the Flatté formula. The dashed dotted vertical line shows the position of the $p\overline{p}$ mass threshold, the dots with error bars are data, the solid curves are total fit results, the dashed curves are the state around $1.85\mathrm{GeV}/c^2$, the short-dashed curves are the $f_1(1510)$, the dash-dotted curves are the $X(2120)$, the dash-dot-dot-dotted curves are the $X(1920)$, and the long-dashed curves are nonresonant ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ fit results; the shaded histograms are background events. The inset shows the data and the global fit between 1.8 and $1.95\mathrm{GeV}/c^2$.

Figure 4

Fit results of using a coherent sum of two Breit-Wigner amplitudes. The dashed dotted vertical line shows the position of the $p\overline{p}$ mass threshold, the dots with error bars are data, the solid curves are total fit results, the dashed curves are the sum of $X(1835)$ and $X(1870)$, the short-dashed curves are the $f_1(1510)$, the dash-dotted curves are the $X(2120)$, the long-dashed curves are nonresonant ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ fit results, and the shaded histograms are background events. The inset shows the data and the global fit between 1.8 and $1.95\mathrm{GeV}/c^2$.