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The effect of the photon emission (bremsstrahlung) in the cross section ofthe process of direct production of the Higgs boson in the future highluminosity electron and muon colliders is calculated. It was found that crosssection at the top of the Higgs boson resonance peak is reduced by factor 0.347for the electron collider and 0.548 for the muon collider. Machine spread ofthe centre of the mass energy of 4.2MeV (equal to the Higgs width) would reducepeak cross section further, by factor 0.170 and 0.256 (QED and energy spread)for electron and muon beams respectively. Possible uncertainties in theresummed QED calculations are discussed. Numerical results for the lineshapecross section including QED and many values of the machine energy spread areprovided.

Lineshape of the Higgs boson in future lepton colliders