Analysis of the process \(e^{+}e^{-}\rightarrow \mu ^{+} \mu ^{-}\) in the presence of a linearly polarized electromagnetic field

In the centre of mass frame, we have investigated the electroweak process \({e}^{+}{e}^{-}\rightarrow \mu ^{+}\mu ^{-}\) $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the presence of a plane and monochromatic laser wave of linear polarization. We provide the theoretical calculations of the differential cross-section for this process by using the scattering-matrix approach and Dirac-Volkov formalism. The laser-assisted cross-section is computed, and its dependence on the laser parameters is analyzed. We have found that this cross-section increases significantly inside a linearly polarized laser wave co-propagating with the incident particle’s beam, and it passes its corresponding laser-free cross-section by several orders of magnitude.