Exclusive Leptonium Electroproduction

Abstract

Purely leptonic bound states provide precision probes of QED. Positronium $(e^{+}{e}^{-})$ and muonium $({\mu }^{+}{e}^{-})$ have long been observed, whereas dimuonium $({\mu }^{+}{\mu }^{-})$ and tauonium $({\tau }^{+}{\tau }^{-})$ remain undiscovered. We study exclusive vector-leptonium electroproduction in $ep$ collisions within nonrelativistic QED. We include the Bethe--Heitler and double deeply virtual Compton scattering contributions and their interference, and calculate the NLO QCD hard-scattering kernels entering the dominant Compton form factor $\Hcal$ within collinear GPD factorization. The NLO QCD correction to the DDVCS contribution changes from a strong suppression at low photon virtuality to a sizable enhancement as the lower virtuality cut is raised, with the gluon channel providing the dominant contribution. Bethe--Heitler production dominates the exclusive rate, supporting dedicated dimuonium searches at the EIC and JLab, with larger samples expected at higher-energy electron--proton colliders. The much larger positronium samples provide a high-statistics environment for precision QED studies, whereas tauonium production remains strongly suppressed.

21 pages, 6 figures