Dynamical symmetry breaking with a fourth generation

Abstract

Adding a fourth generation to the standard model and assuming it to be valid up to some cutoff $\ensuremath{\Lambda}$, we show that electroweak symmetry is broken by radiative corrections due to the fourth generation. The effects of the fourth generation are isolated using a Lagrangian with a genuine scalar without self-interactions at the classical level. For masses of the fourth generation consistent with electroweak precision data (including the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ $CP$ asymmetries), we obtain a Higgs mass of the order of a few hundreds GeV and a cutoff $\ensuremath{\Lambda}$ around 1--2 TeV. We study the reliability of the perturbative treatment used to obtain these results taking into account the running of the Yukawa couplings of the fourth quark generation with the aid of the renormalization group equations, finding similar allowed values for the Higgs mass but a slightly lower cutoff due to the breaking of the perturbative regime. Such low cutoff means that the effects of new physics needed to describe electroweak interactions at energy above $\ensuremath{\Lambda}$ should be measurable at the LHC. We use the minimal supersymmetric extension of the standard model with four generations as an explicit example of models realizing the dynamical electroweak symmetry breaking by radiative corrections and containing new physics. Here, the cutoff is replaced by the masses of the squarks and electroweak symmetry breaking by radiative corrections requires the squark masses to be of the order of 1 TeV.