Muon pair production in the process $e^{+}+e^{-}\to e^{+}+e^{-}+{\mu }^{+}+{\mu }^{-}$ by the two-photon collisions $\gamma \gamma \to {\mu }^{+}{\mu }^{-}$ at high energies. The transverse momentum distributions

In this present paper, we investigate the muon pairs production in the interaction between two quasireal photons in $e^{+}{e}^{-}$ collision. The total and differential cross section of the process $\gamma \gamma \to {\mu }^{+}{\mu }^{-}$ at a beam energy of photons from 3 GeV to 40 GeV in the center-of-mass and for different values of muon transverse momentum and the muon rapidity and the muon angle are calculated. We also study the total cross section, as a function of the $e^{+}{e}^{-}$ center-of-mass energy $\sqrt{s}$ in the region 5 GeV $\leq \sqrt {s} \leq$209GeVprocessofthe$e^+ +e^- \to e^+ + e^- +\mu^+ + \mu^-$ by the two-photon mechanism. The obtained our results are in satisfactory agreement with the experimental data.