We report a measurement of the cross section for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ 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 $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ is determined to be ${\mathrm{\Gamma }}_{ee}\times \mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )<7.5\times {10}^{-3}\mathrm{eV}$ at 90% confidence level under an assumption of total width of $1.19\pm 0.21\mathrm{MeV}$. This is an improvement of a factor of about 17 compared to the previous limit. Furthermore, using the latest result of $\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )$, an upper limit on the electronic width ${\mathrm{\Gamma }}_{ee}$ of $X(3872)$ is obtained to be $<0.32\mathrm{eV}$ at the 90% confidence level.

• Received 24 September 2022
• Accepted 10 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.032007

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Published by the American Physical Society