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The particle discovered in the Higgs boson searches at the LHC with a mass ofabout 125 GeV is compatible within the present uncertainties with the Higgsboson predicted in the Standard Model (SM), but it could also be identifiedwith one of the neutral Higgs bosons in a variety of Beyond the SM (BSM)theories with an extended Higgs sector. The possibility that an additionalHiggs boson (or even more than one) could be lighter than the state that hasbeen detected at 125 GeV occurs generically in many BSM models and has somesupport from slight excesses that were observed above the backgroundexpectations in Higgs searches at LEP and at the LHC. The couplings betweenadditional Higgs fields and the electroweak gauge bosons in BSM theories couldbe probed by model-independent Higgs searches at lepton colliders. We present agenerator-level extrapolation of the limits obtained at LEP to the case of afuture $e^+e^-$ collider, both for the search where the light Higgs bosondecays into a pair of bottom quarks and for the decay-mode-independent searchutilising the recoil method. We find that at the ILC with a c.m. energy of 250GeV, an integrated luminosity of 500 fb^{-1} and polarised beams, thesensitivity to a light Higgs boson with reduced couplings to gauge bosons isimproved by more than an order of magnitude compared to the LEP limits and goesmuch beyond the projected indirect sensitivity of the HL-LHC with 3000 fb^{-1}from the rate measurements of the detected state at 125 GeV.

Prospects for direct searches for light Higgs bosons at the ILC with 250 GeV