Muon pair production in relativistic nuclear collisions

The exclusive production of one $\mu^+\mu^-$ pair in collisions of two ultra-relativistic nuclei is considered. We present the simple method for calculation of the Born cross section for this process. Then we found that the Coulomb corrections to this cross section (which correspond to multi-photon exchange of the produced $\mu^{\pm}$ with nuclei) are small while the unitarity corrections are large. This is in sharp contrast to the exclusive $e^+e^-$ pair production where the Coulomb corrections to the Born cross section are large while the unitarity corrections are small. We calculated also the cross section for the production of one $\mu^+\mu^-$ pair and several $e^+e^-$ pairs in the leading logarithmic approximation. Using this cross section we found that the inclusive production of $\mu^+\mu^-$ pair coincides in this approximation with its Born value.