Production of leptonium in heavy quarkonium decays

Abstract: The lepton pair with opposite charges can form the bound state called ``leptonium'' with quantum electrodynamics interaction. The heavy quarkonium like $J/\psi$ can be massively produced at the BESIII and the future Super Tau-Charm Facility (STCF). We study the production of leptonium in heavy quarkonium decays, $${\cal{Q}} \longrightarrow (l_1⁺ l_2^-)[n] +\gamma$$ ($l_{1,2}= \tau,\, \mu,\, e$) and $${\cal{Q}} \longrightarrow (l_1⁺ l_2^-)[n] + l_1^- l_2<sup>+$$, where ${\cal{Q}}$ is the heavy quarkonium $J/\psi$ or $\Upsilon$, $n=$ ${<sup>1S_0}$ or $<sup>3S_1$ refer to the para- and ortho-leptonium respectively. With the annual production of $3.4 \times 10<sup>{12}$ $J/\psi$ events at STCF, it is very promising to make some observations on the positronium $(e<sup>+e<sup>-)$, the muonium $(\mu<sup>+e<sup>-)$, and the dimuonium $(\mu<sup>+\mu<sup>-)$. Specifically, the ortho-dimuonium $(\mu<sup>+\mu<sup>-)[<sup>3S_1]$ might be discovered at future STCF with the inclusive branching fraction $$Br(J/\psi \longrightarrow (\mu^{+\mu^{-)[^3S_1]}} +X) = 1.5 \times 10<sup>{-12}$$.