Spin-Parity Analysis of $p\overline{p}$ Mass Threshold Structure in $J/\psi$ and $\psi (3686)$ Radiative Decays

A partial wave analysis of the $p\overline{p}$ mass-threshold enhancement in the reaction $J/\psi \to \gamma p\overline{p}$ is used to determine its $J^{\mathrm{PC}}$ quantum numbers to be $0^{-+}$, its peak mass to be below threshold at $M={1832}_{-5}^{+19}(\mathrm{stat}{)}_{-17}^{+18}(\mathrm{syst})\pm 19(\mathrm{model})\mathrm{MeV}/c^2$, and its total width to be $\Gamma <76\mathrm{MeV}/c^2$ at the 90% C.L. The product of branching ratios is measured to be $\mathrm{BR}[J/\psi \to \gamma X(p\overline{p})]\mathrm{BR}[X(p\overline{p})\to p\overline{p}]=[{9.0}_{-1.1}^{+0.4}(\mathrm{stat}{)}_{-5.0}^{+1.5}(\mathrm{syst})\pm 2.3(\mathrm{model})]\times {10}^{-5}$. A similar analysis performed on $\psi (3686)\to \gamma p\overline{p}$ decays shows, for the first time, the presence of a corresponding enhancement with a production rate relative to that for $J/\psi$ decays of $R=[{5.08}_{-0.45}^{+0.71}(\mathrm{stat}{)}_{-3.58}^{+0.67}(\mathrm{syst})\pm 0.12(\mathrm{model})]\%$.

Figure 1

The $p\overline{p}$ invariant mass spectrum for the selected $J/\psi \to \gamma p\overline{p}$ candidate events. (a) The $p\overline{p}$ invariant mass spectrum; the open histogram is data and the dashed line is from $J/\psi \to \gamma p\overline{p}$ phase-space MC events (with arbitrary normalization). (b) An $M^2(\gamma p)$ (horizontal) versus $M^2(\gamma \overline{p})$ (vertical) Dalitz plot for the selected events.

Figure 2

Comparisons between data and PWA fit projection: (a) the $p\overline{p}$ invariant mass; (b)–(d) the polar angle ${\theta }_{\gamma }$ of the radiative photon in the $J/\psi$ center of mass system, the polar angle ${\theta }_p$ and the azimuthal angle ${\varphi }_p$ of the proton in the $p\overline{p}$ center of mass system with $M_{p\overline{p}}-2m_p<50\mathrm{MeV}/c^2$, respectively. Here, the black dots with error bars are data, the solid histograms show the PWA total projection, and the dashed, dotted, dash-dotted, and dash-dot-dotted lines show the contributions of the $X(p\overline{p})$, $0^{++}$ phase space, $f_0(2100)$ and $f_2(1910)$, respectively.

Figure 3

(a) The $p\overline{p}$ invariant mass spectrum for the selected $\psi (3686)\to \gamma p\overline{p}$ candidate events; the open histogram is data and the dashed line is from a $\psi (3686)\to \gamma p\overline{p}$ phase-space MC events (with arbitrary normalization). (b) Comparisons between data and PWA fit projection for $p\overline{p}$ mass spectrum, the representations of the error bars and histograms are same as those in Fig. 2.