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$J / ψ$ electromagnetic production associated with light hadrons at $B$ factories

The electromagnetic productions of $J ψ$ associated with light hadrons(LH) and leptonic pairs($μ^+μ^-$, $τ^+τ^-$) at $B$ factories are studied. We find that the direct electromagnetic production cross sections of $J / ψ$($ψ(2S)$) associated with light hadrons is about $0.10(0.04)$ pb. The direct production cross sections of $J / ψ$($ψ(2S)$) associated with $μ^+μ^-$ is about $0.056(0.020)$ pb. If we include the contributions from $ψ(2S)$ decay, we can get the prompt cross section $σ[e^+e^- \to J/ψ+μ^+μ^-]=(0.068 \pm 0.002)$ pb, about $(16 \pm 5) %$ of the Belle data $σ[e^+e^- \to J/ψ+X_{non-c\bar c}]=(0.43\pm 0.09\pm 0.09)$ pb, meanwhile the $e^+e^- \to J/ψ+τ^+τ^-$ process only contributes $2 %$. The prompt cross section $σ[e^+e^- \to J/ψ+Light Hadrons]=(0.121 \pm 0.005)$ pb is about $(28 \pm 8) %$ of the Belle data.