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

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