Higgs production in $e$ and real $\gamma$ collision

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