η transitions between charmonia with meson loop contributions

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

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