An Improved Limit for Gamma_ee of X(3872) and Gamma_ee Measurement of psi(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- -> gamma_ISR X(3872) -> gamma_ISR pi+pi-J/psi 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 Gamma_ee^X(3872)Br(X(3872) -> pi+pi-J\psi) < 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 psi(3686) to be Gamma_ee^psi(3686) = 2231 +- 18 +- 99 eV.