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Double $J/\psi$ production in $e^+e^-$ collisions involving colour-octetchannels are evaluated up to order $\alpha^2\alpha_s^3$. Having implemented thevariation of the parameters ($m_c$, $\mu_r$ and long-distance matrix elements),we found that the cross sections for producing double $J/\psi$ at B-factoriesrange from $-0.016$fb to $0.245$fb, which are even much smaller than that viathe colour-siglet mechanism. Accordingly, this result is consistent with themeasurement by the Belle and BABAR Collaborations.

Is the colour-octet mechanism consistent with the double $J/\psi$ production measurement at B-factories?