  It is widely believed that, for a given Top mass, the Higgs mass has a lower
bound: if m_Higgs is too small, the Higgs vacuum is unstable due to Top
dynamics. From vacuum instability, the state-of-the-art calculation of the
lower bound is close to the current experimental limit. Using non-perturbative
simulations and large N calculations, we show that the vacuum is in fact never
unstable. Instead, we investigate the existence of a new lower bound, based on
the intrinsic cut-off of this trivial theory.
