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We study the Higgs self couplings of a supersymmetric $E_6$ model that hastwo Higgs doublets and two Higgs singlets. The lightest scalar Higgs boson inthe model may be heavier than 112 GeV, at the one-loop level, where thenegative results for the Higgs search at the LEP2 experiments are taken intoaccount. The contributions from the top and scalar top quark loops are includedin the radiative corrections to the one-loop mass of the lightest scalar Higgsboson, in the effective potential approximation. The effect of the Higgs selfcouplings may be observed in the production of the lightest scalar Higgs bosonsin $e^+e^-$ collisions at the International Linear Collider (ILC) via doubleHiggs-strahlung process. For the center of mass energy of 500 GeV with theintegrated luminosity of 500 fb$^{-1}$ and the efficiency of 20 %, we expectthat at least 5 events of the lightest scalar Higgs boson may be produced atthe ILC via double Higgs-strahlung process.

Study of Higgs self couplings of a supersymmetric $E_6$ model at the International Linear Collider