Production of leptonium in heavy quarkonium decays

Lepton pairs with opposite charges can form bound states known as ``leptonium'' through quantum electrodynamic interactions. Heavy quarkonia such as $J/\psi$ are abundantly produced at facilities like BESIII and the future Super Tau-Charm Facility (STCF). In this work, we investigate leptonium production in heavy quarkonium decays, specifically focusing on the processes ${\cal{Q}} \longrightarrow (l_1^+ l_2^-)[n] +\gamma$ ($l_{1,2}= \tau,\, \mu,\, e$) and ${\cal{Q}} \longrightarrow (l_1^+ l_2^-)[n] + l_1^- l_2^+$. Here, ${\cal{Q}}$ denotes the heavy quarkonium $J/\psi$ or $\Upsilon$, while $n=$ ${^1S_0}$ or $^3S_1$ corresponds to para-leptonium and ortho-leptonium, respectively. With an annual production of $3.4 \times 10^{12}$ $J/\psi$ events at STCF, there is significant potential to observe positronium $(e^+e^-)$, muonium $(\mu^+e^-)$, and dimuonium $(\mu^+\mu^-)$. In particular, the ortho-dimuonium $(\mu^+\mu^-)[^3S_1]$ may be discovered at the future STCF, with an inclusive branching fraction of $Br(J/\psi \longrightarrow (\mu^+\mu^-)[^3S_1] +X) = 1.5 \times 10^{-12}$.