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We discuss complementarity of discovery reaches of heavier neutral Higgsbosons and charged Higgs bosons at the LHC and the International LinearCollider (ILC) in two Higgs doublet models (2HDMs). We perform a comprehensiveanalysis on their production and decay processes for all types of Yukawainteraction under the softly-broken discrete symmetry which is introduced toavoid flavour changing neutral currents, and we investigate parameter spaces ofdiscovering additional Higgs bosons at the ILC beyond the LHC reach. We findthat the 500 GeV run of the ILC with the integrated luminosity of 500 fb^{-1}shows an advantage for discovering the additional Higgs bosons in the regionwhere the LHC cannot discover them with the integrated luminosity of 300fb^{-1}. For the 1 TeV run of the ILC with the integrated luminosity of 1ab^{-1}, production processes of an additional Higgs boson associated with thetop quark can be useful as discovery channels in some parameter spaces wherethe LHC with the integrated luminosity of 3000 fb^{-1} cannot reach. It isemphasized that the complementary study at the LHC and the ILC is useful notonly to survey additional Higgs bosons at the TeV scale, but also todiscriminate types of Yukawa interaction in the 2HDM.

Complementarity in direct searches for additional Higgs bosons at the LHC and the International Linear Collider