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