Exclusive and inclusive muon pair production in collisions of relativistic nuclei

The exclusive production of one ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair in collisions of two ultrarelativistic nuclei is considered. We present a simple method for the calculation of the Born cross section for this process based on an improved equivalent photon approximation. We find that the Coulomb corrections to this cross section (corresponding to multiphoton exchange of the produced ${\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}$ with the nuclei) are small, whereas the unitarity corrections (corresponding to the exchange of light-by-light blocks between nuclei) are large. This is in sharp contrast to the exclusive ${e}^{+}{e}^{\ensuremath{-}}$ pair production where the Coulomb corrections to the Born cross section are large, whereas the unitarity corrections are small. We calculate also the cross section for the production of one ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair and several ${e}^{+}{e}^{\ensuremath{-}}$ pairs in the leading logarithmic approximation. Using this cross section we find that the inclusive production of ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair coincides in this approximation with its Born value.