\eta\ transitions between charmonia with meson loop contributions

Abstract

We study the $\eta$ transitions between $\psi (4040/4160)$ and $J/\psi$ by introducing charmed meson loops in an effective Lagrangian approach to enhance the decay amplitudes. The branching fractions $\mathcal{B}[\psi (4040)\to J/\psi \eta ]$ and $\mathcal{B}[\psi (4160)\to J/\psi \eta ]$ estimated in this paper can remarkably explain the experimental measurements of Belle and BESIII within a reasonable parameter range. The ${\eta }^{\prime }$ transition between $\psi (4160)$ and $J/\psi$ is also investigated, and the branching fraction is under the upper limit of CLEO, which can be tested by future experiments.

Comments: 6 pages, 4 figures. More contents and discussions added. Typos corrected. Accepted by Phys. Rev. D