Effect of the laser beam geometry on laser-assisted muon pair production process at e+e− collider

In this research paper, we have investigated the process of muon pair production in high energy e+e− collisions via the exchange of γ and Z-bosons in the presence of the laser field for different directions. Analytical calculations of the cross-section are done within the scattering matrix approach by using the Dirac-Volkov states for electron and positron. The numerical computation of the cross-section shows that it behaves differently by changing the laser wave direction. For a laser field propagating in parallel with the incident beam, the cross-section is strongly affected from low intensities. In addition, for a given laser field strength and frequency, the required number of photons to be transferred increases by increasing the centre of mass energy. Therefore, the acceleration gradient provided by a collinear laser field further enhances the centre of mass energy.