  In this paper, we have investigated the elementary particle reaction ${e}^{+}
{e}^{-} \rightarrow{\mu}^{+} {\mu}^{-}$ that results from the electron-positron
interaction, at the leading order, with an intense laser wave of circular
polarization. We have derived, by annalytical means, the laser-assisted
differential cross section expression by using the scattering matrix approach.
We have analyzed the energy and the number of exchanged photons dependence of
muon pair production in electron-positron annihilation at different centre of
mass energies including the $Z$-boson peak. For this reason, a wide range of
high centre of mass energies relevant to future $e^{+}e^{-}$ collider were
covered to study the cross section behavior. We have found that, for a given
number of exchanged photons, laser field strength and frequency, the circularly
polarized laser field decreases the total cross section by several orders of
magnitudes.
