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

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.

14.80.Bn
98.80.Cq
95.30.Cq
grand unified theory
renormalization group
cosmological constant
vacuum state: fluctuation
field theory: massive
Higgs particle: mass
spontaneous symmetry breaking

References(20)

Figures(0)

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