  The renormalization-group equation for the zero-point energies associated
with vacuum fluctuations of massive fields from the Standard Model is examined.
Our main observation is that at any scale the running is necessarily dominated
by the heaviest degrees of freedom, in clear contradistinction with the
Appelquist & Carazzone decoupling theorem. Such an enhanced running would
represent a disaster for cosmology, unless a fine-tuned relation among the
masses of heavy particles is imposed. In this way, we obtain $m_H \simeq 550
GeV$ for the Higgs mass, a value safely within the unitarity bound, but far
above the more stringent triviality bound for the case when the validity of the
Standard Model is pushed up to the grand unification (or Planck) scale.
