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Sensitivity of the decay $h\to ZZ^*\to Zl+l-$ to the Higgs self coupling through radiative corrections

We study the radiative corrections induced by the triple Higgs boson coupling $hhh$ in the three body decay $h\to ZZ^*\to Zl\bar l$. We show that these corrections are potentially sensitive to the specific value of this coupling in the Standard Model and the Two Higgs Doublet Model (2HDM). These effects may induce corrections to the integrated decay width of the three-body decay of order few percent in the 2HDM and thus open a new window to test the Higgs boson self interaction in physics beyond the standard model.