Four-lepton decays of neutral vector mesons

We investigate the rare electromagnetic decays of neutral vector mesons (exemplified by $J/\ensuremath{\psi}$, $\mathrm{\ensuremath{\Upsilon}}$, ${\ensuremath{\rho}}^{0}$, $\ensuremath{\omega},\ensuremath{\phi}$, \dots{}) into four charged leptons [$2({e}^{+}{e}^{\ensuremath{-}})$, $2({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$, $2({\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}})$, ${e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, \dots{}] at lowest order in QED. In contrast to the case of vector meson decay into a single pair of leptons, the lepton mass must be retained in these four-lepton decay channels to cut off the mass singularity. Owing to more pronounced collinear enhancement, the branching fractions of vector mesons decays into $2({e}^{+}{e}^{\ensuremath{-}})$ are considerably greater than those for decays into $2({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$. The decay channels $J/\ensuremath{\psi}(\mathrm{\ensuremath{\Upsilon}})\ensuremath{\rightarrow}2({e}^{+}{e}^{\ensuremath{-}}),{e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are predicted to have branching fractions of order ${10}^{\ensuremath{-}5}$, which appear to have bright observation prospect at BESIII, Belle 2, and LHC experiments.

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