then RG-evolve the [[Standard Model ]{}]{}parameters to higher scales as shown in Fig. \[RG-SM-Running\].

![ []{data-label="RG-SM-Running"}](plots/SM.pdf){width="75.00000%"}

Our two-loop results are in good agreement with earlier results up to very small differences due to higher loops and updated initial values compared to the earlier papers. The latter are mainly due to the increased precision of the experimental numbers which has now become available. We stress that an in-depth reanalysis of the [[Standard Model ]{}]{}Higgs is not the main goal of our paper, hence we will not carry out a sensitivity analysis of Higgs vacuum stability and its dependence on the input parameter errors. In fact, in the seesaw scenarios of interest to us, such tiny effects are negligible when compared to the effects of the new Yukawa couplings.

Notice from Fig. \[RG-SM-Running\] that the [[Standard Model ]{}]{}Higgs quartic coupling $\lambda$ becomes negative at $\mu \simeq 10^{10}$ GeV. This would imply that the Higgs potential is unbounded from below and the Higgs vacuum is unstable. A dedicated analysis shows that [[Standard Model ]{}]{}Higgs vacuum is not unstable, but rather metastable[^2] with very long lifetime [@Buttazzo:2013uya; @Espinosa:2015kwx].

However, as already mentioned, the [[Standard Model ]{}]{}cannot be the final theory up to the Planck 