An improved limit for ΓeeΓee of X(3872)X(3872) and ΓeeΓee measurement of ψ(3686)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−→γISRX(3872)→γISRπ+π−J/ψe+e−→γISRX(3872)→γISRπ+π−J/ψ via the Initial State Radiation technique. The production of a resonance with quantum numbers JPC=1++JPC=1++ such as the X(3872)X(3872) via single photon e+e−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)X(3872), and therefore give an upper limit for the electronic width times the branching fraction ΓeeX(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)ψ(3686) to be Γeeψ(3686)=2213±18stat±99sys eV.