In the framework of the electroweak standard model, we investigated, in the center of mass frame, the Higgs boson production in the presence of an intense laser field via e + e − annihilation (e + e − → ZH). By comparing our results with those obtained by Djouadi (2008 Phys. Rept. 457 1) for laser-free process, we show that the circularly polarized laser field affects significantly the s-channel Higgs boson production. We find that for a given number of exchanged photons, laser field strength and frequency, the total cross section decreases by several orders of magnitude. These effects of laser field on cross section are found to be consistent with what was found for muon pair production via QED process in the presence of a circularly polarized laser field (Müller et al 2006 Phys. Rev. D 74 074017).

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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 laser-assisted differential cross section expression by using the scattering matrix approach. We have analysed 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 behaviour. 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.