On the quantum numbers of the $X(1880)$

We study the properties of the $X(1880)$, the structure around the $\bar{p}p$ threshold that appears in the $3(\pi^+\pi^-)$ invariant mass spectrum in the decay process of $J/\psi \to \gamma 3(\pi^+\pi^-)$. Nucleon-antinucleon rescattering is taken into account in our analysis, and the decay amplitude of $J/\psi \to \gamma 3(\pi^+\pi^-)$ can be obtained by the distorted wave Born approximation. With these amplitudes, we analyze the contributions to the $X(1880)$ from different partial waves. Our analysis suggests that the $X(1880)$ should be isoscalar $0^{-+}$, and it is generated by the threshold behavior.