Stability and UV completion of the Standard Model

The knowledge of the electroweak vacuum stability condition is of the greatest importance for our understanding of beyond Standard Model physics. It is widely believed that new physics that lives at very high-energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher-order operators. Here we consider for the first time new physics at extremely high-energy scales (say close to the Planck scale) in terms of renormalizable operators, in other words we consider a sort of toy UV completion of the Standard Model, and definitely show that its presence can be crucial in determining the vacuum stability condition. This result has important phenomenological consequences, as it provides useful guidance in studying beyond Standard Model theories. Moreover, it suggests that very popular speculations based on the so-called "criticality" of the Standard Model do not appear to be well founded.