Exact formulae for Higgs production through eγ → eH in the non-linear Rξ--gauge

We study the production of the SM Higgs boson (H0) at future eγ colliders, through the reaction eγ → eH0. The amplitude is evaluated using the non-linear Rξ-gauge, which greatly simplifies the calculation. Complete analytical expressions for the amplitudes are presented, which include the contributions from 1-loop triangles γγ*H0 and γZ*H0 as well as the W- and Z-boxes with their related eeH0 triangle graphs. The resulting cross section for this mechanism indicates that it could be used to detect the Higgs signal and to test its properties.