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The renormalization-group equation for the zero-point energies associatedwith vacuum fluctuations of massive fields from the Standard Model is examined.Our main observation is that at any scale the running is necessarily dominatedby the heaviest degrees of freedom, in clear contradistinction with theAppelquist & Carazzone decoupling theorem. Such an enhanced running wouldrepresent a disaster for cosmology, unless a fine-tuned relation among themasses of heavy particles is imposed. In this way, we obtain $m_H \simeq 550GeV$ for the Higgs mass, a value safely within the unitarity bound, but farabove the more stringent triviality bound for the case when the validity of theStandard Model is pushed up to the grand unification (or Planck) scale.Comment: 11 pages, LaTex2

Renormalization-group running of the cosmological constant and its implication for the Higgs boson mass in the standard model