Critical Constraints on Chiral Hierarchies

Abstract

We consider the constraints that critical dynamics places on models with a top quark condensate or strong extended technicolor (ETC). These models require that chiral-symmetry-breaking dynamics at a high energy scale plays a significant role in electroweak symmetry breaking. In order for there to be a large hierarchy between the scale of the high energy dynamics and the weak scale, the high energy theory must have a second order chiral phase transition. If the transition is second order, then close to the transition the theory may be described in terms of a low-energy effective Lagrangian with composite ``Higgs'' scalars. However, scalar theories in which there are more than one ${\Phi }^4$ coupling can have a {\it first order} phase transition instead, due to the Coleman-Weinberg instability. Therefore, top-condensate or strong ETC theories in which the composite scalars have more than one ${\Phi }^4$ coupling cannot always support a large hierarchy. In particular, if the Nambu--Jona-Lasinio model solved in the large-$N_c$ limit is a good approximation to the high-energy dynamics, then these models will not produce acceptable electroweak symmetry breaking.

10 pages, 1 postscript figure (appended), BUHEP-92-35, HUTP-92/A058

References in corpus (1)

• A Tumbling Top-Quark Condensate Model

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