Triviality and the Higgs mass lower bound

In the minimal Standard Model, it is commonly believed that the Higgs mass cannot be too small, otherwise Top quark dynamics makes the Higgs potential unstable. Although this Higgs mass lower bound is relevant for current phenomenology, we show that the Higgs vacuum instability in fact does not exist and only appears when treating incorrectly the cut-off in the renormalization of a trivial theory. We also demonstrate how to calculate correctly the regulator-dependent Higgs mass lower bound.