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Higgs production in $e$ and real $γ$ collision

We investigate the Standard Model Higgs boson production in $e^-γ$ collision. The electroweak one-loop contributions to the scattering amplitude for $e^-γ\rightarrow e^-H$ are calculated and expressed in analytical form. We analyze the cross section for the Higgs production in $e^-γ$ collision for each combination of polarizations of the initial electron and photon beams. The feasibility of observing the Higgs boson in $e^-+γ\rightarrow e^-+b+{\overline b}$ channel is examined.