Some properties of the newly observed X(1835) state at BES

Abstract

Recently the BES collaboration has announced observation of a resonant state in the $π^+π^- η'$ spectrum in $J/ψ\to γπ^+π^-η'$ decay. Fitting the data with a $0^{-+}$ state, the mass is determined to be 1833.7 MeV with $7.7σ$ statistic significance. This state is consistent with the one extracted from previously reported $p \bar p$ threshold enhancement data in $J/ψ\to γp \bar p$. We study the properties of this state using QCD anomaly and QCD sum rules assuming X(1835) to be a pseudoscalar and show that it is consistent with data. We find that this state has a sizeable matrix element $<0|G\tilde G|G_p>$ leading to branching ratios of $(2.61\sim 7.37)\times 10^{-3}$ and $(2.21\sim 10.61)\times 10^{-2}$ for $J/ψ\to γG_p$ and for $G_p \to π^+π^- η'$, respectively. Combining the calculated branching ratio of $J/ψ\to γG_p$ and data on threshold enhancement in $J/ψ\to γp \bar p$, we determine the coupling for $G_p- p-\bar p$ interaction. We finally study branching ratios of other $J/ψ\to γ+ {three mesons}$ decay modes. We find that $J/ψ\to γG_p \to γ(π^+π^- η, K K π^0)$ can provide useful tests for the mechanism proposed.

13 pages, 3 figures. The final version to appear at EPJC