The muon pair production in the process

In the present paper, we investigate the muon pair production in the interaction between two quasi-real photons in $$e^+e^-$$ collision. We calculate the total and differential cross section of the process $$\gamma \gamma \rightarrow \mu ^+\mu ^-$$ at a beam energy of photons from 3 to 40 GeV in the center-of-mass and for different values of the muon transverse momentum, the muon rapidity and the muon angle. In the $$\gamma \gamma \rightarrow \mu ^+\mu ^-$$ process we also take the contribution of the Box+Vertex correction+ Soft photon emission+Vacuum polarization diagrams. We also study the cross section of the $$e^+ +e^- \rightarrow e^+ + e^- +\mu ^+ + \mu ^-$$ process as a function of the $$e^+ e^-$$ center-of-mass energy $$\sqrt{s}$$ in the region 5 GeV $$\le \sqrt{s} \le $$ 209 GeV using the two-photon mechanism. The obtained results are in satisfactory agreement with experimental data