TOP CONDENSATES AS HIGGS SUBSTITUTE

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Abstract
We review developments in top condensation starting from the first example which was a simple effective Nambu–Jona-Lasinio (NJL) model. The connection between the underlying four-fermion interaction and the structure of the composite Higgs sector is generalized to obtain the scalar sectors of a number of Standard Model extensions dynamically from some NJL model, as well as to include possible radial and spin excitations of the Higgs sector. In all these NJL models the symmetries do not forbid further higher dimensional four-fermion operators. If such operators could have arbitrary strength then this would result in arbitrary Higgs and top mass predictions. The nonrenormalizable NJL model is however thought to be only an effective description of some fully consistent theory where higher dimensional operators are not free parameters so that the corresponding four-fermion operators are restricted. We discuss renormalizable gauge theories of top condensation where this is the case. These models are therefore predictive and do not lead to arbitrary predictions.
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