Tumbling and technicolor theory.

The extended technicolor theory is a candidate of the physics beyond the standard model. To explain the mass hierarchy of the quarks and leptons, the extended technicolor gauge symmetry must hierarchically break to the technicolor gauge symmetry. Tumbling gauge theory is considered as a candidate of the dynamics of such hierarchical symmetry breaking, since the sequential self-breaking of the gauge symmetry (“tumbling”) can be expected in that theory. It is well known that the extended technicolor theory induces too strong flavorchanging neutral current interactions to be consistent with the experiments. This problem can be solved if the technicolor dynamics is the special one with very large anomalous dimension of the composite operator T̄ T composed by the technifermion field T . Two types of the models with large anomalous dimension have been proposed. One is the gauge theory with slowly running coupling, another is the gauge theory with strong four fermion interaction. It is expected that the large anomalous dimension is realized in the tumbling gauge theory. In this thesis we systematically estimate the strength of the effective four fermion interactions induced in the tumbling gauge theory by using the effective action within the one-gauge-boson-exchange approximation. It is shown that the couplings of the effective four fermion interactions cannot be large enough to realize sufficiently large anomalous dimension. This result is important for the model building of the extended technicolor theory. The decoupling of the gauge bosons and fermions which get their masses in the process of tumbling is also discussed. It is non-perturbatively shown that their effect on the low energy dynamics is negligibly small. Before the estimations, we give the explanation of the fundamental techniques to treat the dynamical symmetry breaking. The scenario and the phenomenology of the extended technicolor theory is also reviewed. The restriction on the extended technicolor theory from the precision experiments is discussed. It is emphasized that the non-oblique correction is important as well as the oblique correction, since the top quark is heavy.