Vector meson production associated with a lepton pair in $e^+$ $e^-$ annihilation

In this work, we investigate a novel production mechanism of vector mesons, exemplified by the production of a neutral vector meson associated with a lepton pair in $e^+e^-$ annihilation, i.e., $e^+e^-\to V l^+l^-$ ($V=J/\psi, \rho^0, \omega, \phi$, and $l=\mu, \tau$). These vector meson production channels can be precisely accounted within QED. The production rates of these processes are dominated by those diagrams where the vector meson is emitted from either the incident electron or positron, which exhibit a $\ln^2 m_l^2$ enhancement stemming from the triple collinear limit of leptons. Our numerical analysis indicates that the corresponding production rates are substantial enough to warrant the observation of these novel vector meson production channels at BESIII and Belle II experiments in near future.