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Photoproduction of relativistic QED bound states in hadronic collisions

In this paper we investigate the photoproduction of QED bound states in proton -- proton, proton -- nucleus and nucleus -- nucleus collisions at RHIC, LHC and FCC energies considering an accurate treatment of the absorptive corrections and for the nuclear form factor. The total cross sections for the production of singlet and triplet $(l^+ l^-)$ states, with $l = e,\, μ, \, τ$, are estimated and a detailed analysis of the photoproduction of singlet QED bound states is performed considering the rapidity ranges covered by central and forward detectors. The impact of the Coulomb corrections on the parapositronium production in heavy ion collisions is estimated. We predict a large number of events associated to the production of ($e^+ e^-$) and ($μ^+ μ^-$) states in hadronic collisions.