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Inspired by the obvious discrepancies between experiment and non-relativisticQCD (NRQCD) studies of $e^+ e^-\to J/\psi+\eta_c$ at $\sqrt{s}\simeq 10.6$ GeV,we investigate contributions from intermediate meson loops as long-rangeinteraction transitions to this process. The intermediate meson loops include$D\bar D(\bar D^\ast)$, $D\bar D^\ast(D {or} D^\ast)$, $D^\ast \bar D^\ast(D)$and corresponding $D_s$ intermediate mesons. With the constraints fromexperimental data on the vertex couplings, we find that the intermediate mesonloops account for $2.7\sim 6.7 fb$ of the cross sections within a reasonablerange of cut-off energies of the factor parameter. We also investigatecontributions from the absorptive part and find that it accounts forapproximately $0.58\sim 1.38 fb$. These results imply that contributions fromlong-range interaction transitions may still play a role in such an energyregion.

Possible contributions to $e^+e^- \to J/\psi + \eta_c$ due to intermediate meson rescatterings