$J/\psi$ production via initial state radiation in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma$ at an $e^{+}{e}^{-}$ center-of-mass energy near 10.6 GeV

We have studied the process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma$ at a center-of-mass energy near the $\mathit{{\rm Y}}\mathrm{}\left(4S\right)\mathrm{}$ resonance for a ${\mu }^{+}{\mu }^{-}$ invariant mass range near the $J/\psi$ mass and measured the cross section $\sigma {(e}^{+}{e}^{-}\to J/\psi \overrightarrow{\gamma }{\mu }^{+}{\mu }^{-}\gamma ).\mathrm{}$ The data set, corresponding to an integrated luminosity of $88.4{\mathrm{fb}}^{-1},$ was collected using the BABAR detector at the SLAC PEP-II collider. From the measured cross section we extract the product $\Gamma (J/\overrightarrow{\psi }{e}^{+}{e}^{-})B(J/\overrightarrow{\psi }{\mu }^{+}{\mu }^{-})=0.330\mathrm{}\pm 0.008\pm 0.007\mathrm{keV}.$ Using the world averages for $B(J/\overrightarrow{\psi }{\mu }^{+}{\mu }^{-})$ and $B(J/\overrightarrow{\psi }{e}^{+}{e}^{-}),$ we derive the $J/\psi$ electronic and total widths: $\Gamma (J/\overrightarrow{\psi }{e}^{+}{e}^{-})=5.61\mathrm{}\pm 0.20\mathrm{keV}$ and $\Gamma =94.7\mathrm{}\pm 4.4\mathrm{keV}.$