Revisiting the decoupling effects in the running of the Cosmological
  Constant
  We revisit the decoupling effects associated with heavy particles in the
renormalization group running of the vacuum energy in a mass-dependent
renormalization scheme. We find the running of the vacuum energy stemming from
the Higgs condensate in the entire energy range and show that it behaves as
expected from the simple dimensional arguments meaning that it exhibits the
quadratic sensitivity to the mass of the heavy particles in the infrared
regime. The consequence of such a running to the fine-tuning problem with the
measured value of the Cosmological Constant is analyzed and the constraint on
the mass spectrum of a given model is derived. We show that in the Standard
Model (SM) this fine-tuning constraint is not satisfied while in the massless
theories this constraint formally coincides with the well known Veltman
condition. We also provide a remarkably simple extension of the SM where
saturation of this constraint enables us to predict the radiative Higgs mass
correctly. Generalization to constant curvature spaces is also given.
