Measurement of the ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi $ cross section in the vicinity of 3.872 GeV

We report a measurement of the cross section for the process ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi $ around the $X\left(3872\right)$ mass in search for the direct formation of ${e}^{+}{e}^{-}\to X\left(3872\right)$ through the two-photon fusion process. No enhancement of the cross section is observed at the $X\left(3872\right)$ peak and an upper limit on the product of electronic width and branching fraction of $X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi $ is determined to be ${\Gamma }_{ee}×B\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)<7.5×{10}^{-3}\text{}\text{}\mathrm{eV}$ at 90% confidence level under an assumption of total width of $1.19±0.21\text{}\text{}\mathrm{MeV}$. This is an improvement of a factor of about 17 compared to the previous limit. Furthermore, using the latest result of $B\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)$, an upper limit on the electronic width ${\Gamma }_{ee}$ of $X\left(3872\right)$ is obtained to be $<0.32\text{}\text{}\mathrm{eV}$ at the 90% confidence level.