Two-loop renormalization group restrictions on the standard model and the fourth chiral family

Abstract.

In the framework of the two-loop renormalization group, the restrictions on the Higgs mass from the electroweak vacuum stability and from the absence of the strong coupling are refined, while the more precise value of the top mass is taken into account. When the SM cutoff is equal to the Planck scale, the Higgs mass must be $M_{\mathrm H} = (161.3 \pm 20.6)^{+4}_{-10}$ GeV and $M_{\mathrm H}\ge 140.7^{+10}_{-10}$ GeV, where the $M_{\mathrm H}$ corridor is the theoretical one and the errors are due to the top-mass uncertainty. The SM two-loop $\beta$ functions are generalized to the case with massive neutrinos from extra families. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck scale excludes a fourth chiral family. Under the precision-experiment restriction $M_{\mathrm H}\leq 215$ GeV, the fourth chiral family, if alone, is excluded even when the SM is regarded as an effective theory. Nevertheless a pair of chiral families constituting a vector-like one could exist.