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We study the decay process of where the relatively clean electromagnetic (EM) transitions appear at leading order at tree level while the hadronic contributions only emerge via hadronic loop transitions. We include the low-lying scalar and pseudoscalar as the dominant contributions in the evaluation of the hadronic loop contributions. It is found that the hadronic effects are negligible comparing with the EM contributions. The decay width of $J/\psi\rightarrow e^+e^- \phi2.12\times 10^{-6}$ keV if there is no any other leading mechanism contributing, and this result will be tested by the BESIII experiment with a large data sample of .

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