Using the data sets taken at center-of-mass energies above 4 GeV by the BESIII detector at the BEPCII storage ring, we search for the reaction e + e ? → γ ISR X ( 3872 ) → γ ISR π + π ? J / ψ via the Initial State Radiation technique. The production of a resonance with quantum numbers J PC = 1 + + such as the X ( 3872 ) via single photon e + e ? annihilation is forbidden, but is allowed by a next-to-leading order box diagram. We do not observe a significant signal of X ( 3872 ) , and therefore give an upper limit for the electronic width times the branching fraction Γ e e X ( 3872 ) B ( X ( 3872 ) → π + π ? J / ψ ) 0.13 ?eV at the 90% confidence level. This measurement improves upon existing limits by a factor of 46. Using the same final state, we also measure the electronic width of the ψ ( 3686 ) to be Γ e e ψ ( 3686 ) = 2213 ± 18 stat ± 99 sys ? eV .
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