NLO corrections to dimuonium production in photon-photon collision

Dimuonium (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>μ</a:mi><a:mo>−</a:mo></a:msup></a:math>) is one of the pure QED bound systems of leptons, together with positronium and ditauonium. The former had been observed in an experiment in 1951 [M. Deutsch, ], while the search for dimuonium and ditauonium (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>τ</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>τ</c:mi><c:mo>−</c:mo></c:msup></c:math>) are still in vain. The ditauonium is thought to be hard to measure due to its short life time, whereas the dimuonium is very likely to be observed in current running experiments. We calculate in this work the para and ortho dimuonium production in photon-photon collision at the next-to-leading order (NLO) in QED. To handle the Coulomb divergence within the bound system, the nonrelativistic QED description is adopted for consistency. The results indicate that the NLO corrections are negative for both para and ortho states, at the normal order of perturbative QED corrections. The measurement of the dimuonium in the Belle II experiment, especially at the forthcoming facility of STCF, is tenable.