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I discuss the stability of the SM scalar potential in view of the discoveryof a Higgs boson with mass around 125 GeV. The role played by the top quarkmass in the choice between the full stability and the metastability conditionsis analyzed in detail. The present experimental value of the top mass do notsupport the possibility that the SM potential is stable up to the Planck scalebut favor an electroweak vacuum sufficiently long-lived to be metastable.

The role of the top quark in the stability of the SM Higgs potential