An improved limit for Γ_ee of X(3872) and Γ_ee measurement of ψ(3686)

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_ISRX(3872)→γ_ISRπ⁺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_ee ^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_ee ^ψ(3686)=2213±18_stat±99_sys eV.