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To understand the direct $J/\psi+X_{\mathrm{non-c\bar{c}}}$ productionmechanism in $e^{+}e^{-}$ annihilation, in this work, we propose to measure theinclusive $J/\psi$ plus light hadrons (LH) production at B-factories andpresent a detailed study on its QED production due to $\psi(2S)$ feed-down,where the $\psi(2S)$ are produced in $e^{+}e^{-}\to \psi(2S)+\gamma$ and$e^{+}e^{-}\to \psi(2S)+f\bar{f}, f=lepton,light quark$, and QED contributionto direct $J/\psi+q\bar{q}$ production with $q=u,d,s$ quark. We find that theQED contribution is huge in the whole phase space region, but can be reducedlargely and is in the same order as the QCD contribution when a suitable cut onthe angel $\theta_{J/\psi}$ between $J/\psi$ and the $e^{+}e^{-}$ beam is made.In this way, the cross section of $J/\psi+LH$ QCD production %which waspredicted theoretical at next-to-leading order QCD together with relativisticcorrection, can be obtained by subtracting the QED contribution from theexperimental measurement on inclusive $J/\psi$ plus light hadrons. To help toremove the QED background, we also calculate the angular and momentumdistribution of $J/\psi$ in the QED contribution.

The QED contribution to $J/\psi$ plus light hadrons production at B-factories