Spin-Parity Analysis of $p\bar{p}$ Mass Threshold Structure in $J/\psi$ and $\psi^\prime$ Radiative Decays

A partial wave analysis of the $p \bar{p}$ mass-threshold enhancement in the reaction $J/\psi\rightarrow\gamma p\bar{p}$ is used to determine: its $J^{PC}$ quantum numbers to be $0^{-+}$; its peak mass to be below threshold at $M=1832^{+19}_{-5} {\rm(stat.)}^{+18}_{-17} {\rm (syst.)}\pm19 {\rm (model)} {\rm MeV}/c^2$; and its total width to be $\Gamma<76 {\rm MeV}/c^2$ at the 90% C.L. The product branching ratio is measured to be $B(J/\psi\rightarrow\gamma X(p\bar{p}))B(X(p\bar{p})\rightarrow p\bar{p})=(9.0^{+0.4}_{-1.1} {\rm (stat.)}^{+1.5}_{-5.0} {\rm (syst.)}\pm2.3 {\rm (model)})\times10^{-5}$. A similar analysis performed on $\psi^\prime\rightarrow\gamma p\bar{p}$ decays shows, for the first time, the presence of a corresponding enhancement with a production rate relative to that for $J/\psi$ decays of $R=(5.08^{+0.71}_{-0.45} {\rm (stat.)}^{+0.67}_{-3.58} {\rm (syst.)}\pm0.12 {\rm (model)})%$.