Fully Radiative Electroweak Symmetry Breaking

Abstract

Models of Gauge-Higgs unification in extra dimensions offer a very elegant playground where one can study electroweak symmetry breaking. The nicest feature is that gauge symmetry itself protects the Higgs potential from divergences, thus potentially curing the hierarchy problem in the Standard Model. In a flat space model tree-level contributions to electroweak precision observables will be absent due to the flatness of the gauge and Higgs wave functions. The Higgs potential is fully radiatively generated and the contribution of bulk fermions will induce a vacuum expectation value. A generic problem is that the quartic scalar coupling is too low, resulting in a Higgs VEV that is too close to the compactification scale, and a Higgs mass that is too light. In this paper we show that it is possible to solve these problems in a minimal scenario by cancellations in the Higgs potential between the contribution of different bulk fermions. A crucial role is played by antiperiodic fermions: the cancellation is not the result of a fine tuning, but rather dictated by the choice of representations and parities of the fermions. We also show that introducing a relatively large representation can help in achieving a sufficiently heavy top. In this case, the strong coupling scale is lowered to a marginally acceptable value, and a more careful analysis of two loop effects should decide if the theory remains under perturbative control.