In the centre of mass frame, we have investigated the process of Higgs production in association with a pair of fermions, e + e − → f f H, at the leading order inside an intense electromagnetic field with circular polarization. Our analytical calculations are based on the Narrow Width Approximation (NWA), which is valid in the leading order. We have considered only the initial particles inside the laser field as a first step. In the second part, we have embedded both initial and final particles in the laser field. We have analyzed the angular distribution of the produced Higgs boson as a function of the laser parameters in both cases. We have found that in the case where both initial and final particles are embedded in the laser field, the order of magnitude of the differential cross-section of the process e + e − → µ + µ − H is reduced more significantly, while that of the process e + e − → ν νH is enhanced.

In this paper, we have investigated the elementary particle reaction e + e − → µ + µ − that results from the electron-positron interaction, at the leading order, with an intense laser wave of circular polarization. We have derived, by analytical means, the laserassisted 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.

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