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We consider a simple Higgs portal model in beyond the standard modelscenario: an extra real gauge singlet scalar that couples to the Higgs. Wecalculate the higher-loop corrections to the cross section of theHiggsstrahlung process $e^+e^- \rightarrow Z h$, along with the tri-Higgscoupling and the wave-function renormalization. We find noticeable contributionto the total Higgsstrahlung cross section, especially coming from two-loopdiagrams. We also find that the correction to the tri-Higgs coupling is complexwhen this extra scalar is lighter than half of the center of mass energy. Itindicates a new source of CP violation. In the region of this extra scalarbeing lighter than a couple of hundreds of GeVs, we argue that the higher-loopcalculation is a more reliable approach than the effective field theorycalculation.

Large Two-loop Effects in the Higgs Sector as New Physics Probes