Initial state radiation effects in inclusive $J/\psi$ production at B factories

Based on Monte Carlo techniques, we analyze the initial state radiation (ISR) effects in prompt $\jpsi$ inclusive production at B factories. ISR enhances cross section $\sigma(e^-e^+\to\jpsi+gg+X)$ by about $15-25\%$, which is almost the same size as the QCD and relativistic correction. Moreover, ISR slightly changes $\sigma(e^-e^+\to\jpsi+c\bar{c}+X)$. The $\jpsi$ momentum spectrum in $e^-e^+\to\jpsi+gg+X$ and in $e^-e^+\to\jpsi+c\bar{c}+X$ is softer after the photon showering from the initial $e^{\pm}$ beam radiation. After combining the QCD,relativistic, and ISR corrections,a more precise theoretical result is obtained. The new result provides a more stringent constraint of the color-octet contribution to $\sigma(e^-e^+\to\jpsi+X_{\rm{non-}c\bar{c}})$.