$J\mathrm{/}\psi$ electromagnetic production associated with light hadrons at $B$ factories

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