μ+μ−-pair production at very low transverse momentum in ultra-peripheral heavy-ion collisions

In recent works that are done at the STAR Collaboration, at small transverse momentum ([Formula: see text] [Formula: see text]MeV/c) region, an excess [Formula: see text]-pair production has been observed in the peripheral collisions of gold–gold and uranium–uranium. Moreover, the ALICE Collaboration reported at low [Formula: see text] a similar excess production of [Formula: see text]-pairs in the peripheral collisions of lead–lead. From the experiments for [Formula: see text]- and [Formula: see text]-pair productions at very low [Formula: see text] that were done at the STAR and ALICE Collaborations, it is pointed out the coherent photon–photon interactions in ultra-peripheral hadronic heavy-ion collisions. In this study, we observed that muon pairs are mostly created in the transverse momentum domain of less than [Formula: see text]-GeV/c transverse momentum region like the electron–positron pairs in ultra-peripheral heavy-ion collisions. For this purpose, the impact parameter-dependent probability equations have been calculated for the STAR experiment Au+Au collisions and for the ALICE experiment Pb+Pb collisions at first. Then, we have calculated the [Formula: see text]-pair production cross-sections for those ions by using the Monte Carlo methods. Also, we showed the differential cross-sections for the Au+Au and Pb+Pb collisions as functions of transverse momentum [Formula: see text], energy [Formula: see text] and invariant mass M of the produced [Formula: see text]-pairs for the given energy levels.