Composite Higgs particles in models with dynamically broken gauge symmetries

This is reason to believe that massive composite (fermion-antifermion) scalar particles closely resembling the usual fundamental Higgs scalar fields exist in theories with dynamically broken gauge symmetries. This composite Higgs couples directly to the fermions in proportion to their masses. Induced couplings to the gauge bosons and self-couplings are calculated as loop effects. The integrals receive significant contributions from asymptotically large momenta and yield invers powers of the gauge coupling constant, a feature that characterizes the nonperturbative nature of the symmetry breaking. The couplings between the composite Higgs and the gauge boson are the same as those in models with fundamental scalars; the two models have identical phenomenology. The self-couplings are determined and fix all parameters associated with the composite scalars. The lowest order results are obtained first with elementary means. A more rigorous derivation that involves calculating the effective action for composite operators follows. Comments regarding extending this work to higher orders and concerning the symmetry-violating solutions to the fermion Schwinger-Dyson equation are given. A possible solution to a longstanding paradox involving non-Abelian gauge boson loops in dynamical symmetry breaking models is offered.