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Abstract:
In this thesis we investigate fundamental features of a mechanism that attempts to explain
the origin of the electroweak scale by the condensation of fermions in high color representations.
Since chiral symmetry in the new fermion sector is dynamically broken due to
non-perturbative effects of the running strong coupling this mechanism provides a natural
explanation for the scale of the condensate by dimensional transmutation. Electroweak
symmetry breaking (EWSB) could then be triggered indirectly via a singlet scalar mediator
which couples to the Standard Model Higgs boson and the new fermion sector. In our
analysis particular focus is put to the impact of the representation on the condensate and
the significance of vector-like fermion masses which explicitly break chiral symmetry. In
doing so, we solve the Dyson-Schwinger equation for the fermion propagator within the
rainbow-approximation and analyze the behavior of the dynamical mass. In the chiral limit,
we find a comparatively larger expectation value (EV) of the condensate for fermions in high
representations than for the fundamental representation. A property reflecting the larger
Casimir invariants of higher representations. For massive fermions, we propose a method to
isolate the non-perturbative contributions to the propagator from the perturbative ones and
calculate a lower bound for the EV of the condensate. Our result suggests that in absolute
numbers the EV of the condensate increases with mass, while its relative contribution to
the dynamical mass diminishes. On the basis of these results, we believe the condensation
of a high color fermion with an explicit mass of the order ~10TeV could successfully create
the scale of EWSB.
