Triviality and the Standard Model

The triviality of the scalar sector of the standard one-doublet Higgs model implies that this model is only an effective low-energy theory valid below some cutoff scale Λ. We show that the experimental constraint on the amount of custodial symmetry violation implies that the scale Λ must be greater than of order 7.5 TeV. The underlying high-energy theory must also include flavor dynamics at a scale of order Λ or greater in order to give rise to the different Yukawa couplings of the Higgs to ordinary fermions. This flavor dynamics will generically produce flavor-changing neutral currents. We show that the experimental constraints on the neutral D-meson mass difference imply that Λ must be greater than of order 21 TeV. For theories defined about the infrared-stable Gaussian fixed-point, we estimate that this lower bound on Λ yields an upper bound of approximately 460 GeV on the Higgs boson's mass, independent of the regulator chosen to define the theory. We also show that some regulator schemes, such as higher-derivative regulators, used to define the theory about a different fixed-point are particularly dangerous because an infinite number of custodial-isospin-violating operators become relevant. 1 In the standard Higgs model, one introduces a fundamental scalar doublet: φ = φ + φ 0 , (1) with potential: V (φ) = λ φ † φ − v 2 2 2. (2) While this theory is simple and renormalizable, it has a number of shortcomings. First, while the theory can be constructed to accommodate the breaking of electroweak symmetry, it provides no explanation for it – one simply assumes that the potential is of the form in eqn. (2). In addition, in the absence of su-persymmetry, quantum corrections to the Higgs mass are naturally of order the largest scale in the theory