Structure around $p\bar{p}$ threshold in $J/\psi$ radiative decays

Abstract

In this paper, we study the structure around the $p\bar{p}$ threshold that appears in $\eta'\pi^+\pi^-$, $3(\pi^+\pi^-)$ and $K_S^0K_S^0\eta$ invariant mass spectra in the processes of relevant $J/\psi$ radiative decays. The $N\bar{N}$ rescattering is taken into account, and the distorted-wave Born approximation is applied to get the decaying amplitude through a two-step process: $J/\psi\to\gamma N\bar{N}\to\gamma\eta'\pi^+\pi^-$, $\gamma 3(\pi^+\pi^-)$ and $\gamma K_S^0K_S^0\eta$. The $N\bar{N}$ scattering amplitudes are obtained by solving the Lippmann-Schwinger equation with the potentials given by chiral effective field theory. To fix the unknown couplings, we fit the amplitudes to the datasets of the latest measurements on the invariant mass spectra of $J/\psi$ radiative decays, as well as the phase shifts and inelasticities given by partial wave analysis. We vary the cutoffs ($R$=0.9, 1.0, and 1.1 fm) and find that the solutions are stable. The structures around $p\bar{p}$ threshold found in the processes of $J/\psi\to\gamma\eta'\pi^+\pi^-$, $J/\psi\to\gamma3(\pi^+\pi^-)$ and $J/\psi\to\gamma K_S^0K_S^0\eta$ can be attributed to threshold behavior of $N\bar{N}$ intermediate states.