Critical constraints on chiral hierarchies

Critical dynamics constrains models of dynamical electroweak symmetry breaking in which the scale of high-energy physics is far above 1 TeV. A big hierarchy requires the high-energy theory to have a second-order chiral phase transition, near which the theory is described by a low-energy effective Lagrangian with composite ``Higgs'' scalars. As scalar theories with more than one Φ⁴ coupling can have a Coleman-Weinberg instability and a first-order transition, such dynamical EWSB models cannot always support a large hierarchy. If the large-Nc Nambu--Jona-Lasinio model is a good approximation to the top-condensate and strong extended technicolor models, they will not produce acceptable EWSB.