In this report we begin by reviewing the phenomenological problems which have originally motivated the introduction of a now strongly interacting ’Technicolor’ sector beyond the Standard Model. The origin of electroweak gauge boson masses is the central theme in Technicolor model building as well as many other extensions of the Standard Model. The starting point in this work is a bottom up approach to W and Z masses where we naïvely assign masses without any underlying Higgs mechanism. We see that this will give problems with perturbative unitarity at high energies. We then introduce the Standard Model Higgs field and demonstrate that this will cure the unitarity issues.
The Standard Model, and in particular the Higgs sector, comes with its own problems. We will review how a strongly interacting Technicolor sector replacing the Higgs can alleviate some of these problems. In particular the Hierarchy problem.
The constraints on a strongly interacting sector beyond the Standard Model will be briefly reviewed. We will argue from the experimental fact that flavor changing neutral currents are strongly suppressed, that Technicolor models must have a renormalized coupling which varies slowly with the renormalization scale. Other constraints come from electroweak precision observables. The Peskin-Takeushi parameters are briefly introduced and we argue that the experimental constraints on the S parameter require the Technicolor sector to be small. We discuss the thermal corrections to the S parameter which could be relevant for future determinations of the quantity from lattice simulations. Also past determinations of the S parameter on the lattice are briefly discussed in light of our results.
After the reviewing part we concentrate on an SO(4) gauge theory with one fermion doublet in the fundamental representation. With this model we explicitly discuss S parameter constraints and renormalization of the gauge coupling. Also it is showed how to implement it in the Standard Model and we compute the running of the Standard Model couplings. The breaking pattern of chiral symmetry is discussed and the low energy operators are worked out in detail.
Results from Monte Carlo simulations of the SO(4) model on the lattice with Wilson fermions are presented. We outline a rough lattice phase diagram and find (weak) indications of chiral symmetry breaking taking place. We discuss finite size effects and discover in small volumes the existence of domain walls separating regions with zero and non-zero expectation value for the Polyakov loops.
The thesis contains some unpublished results, and cannot currently be downloaded from our home page. Please contact Ulrik I. Søndergaard for further information.