Vacuum Stability and Two Loop Threshold Corrections to the Higgs Quartic Coupling

We review the vacuum stability problem in the Standard Model by studying the next-to-next-to-leading order (NNLO) shape of the renormalization group improved effective potential by including the threshold corrections of the SM couplings. For this purpose we computed the sum of the vacuum bubbles diagrams up two-loop level and the Higgs tadpoles contributions by two different methods in an on-shell renormalization scheme where the renormalized parameters are directly expressed in terms of physical observables.