Electroweak symmetry breaking and fermion masses from extra dimensions

TL;DR

The paper develops non-supersymmetric 5D orbifold models in which the Higgs arises from the internal component of a gauge field and analyzes whether realistic Yukawa structures and a viable Higgs potential can be achieved. It shows that boundary-localized fermions, coupled to heavy bulk fermions, generate non-local Yukawa interactions and a finite one-loop Higgs potential via Wilson-line dynamics, with the electroweak scale set by the radius $R$ and the Wilson-line phase $\alpha$. A minimal 5D prototype with SU(3) gauge symmetry illustrates the challenges: the predicted $1/R$, Higgs mass $m_H$, and top mass are too small, though the mechanism remains attractive; adding bulk fermions in large representations or localized gauge kinetic terms can improve the situation but introduce new theoretical and phenomenological tensions, such as non-universal gauge couplings and constraints from the $\rho$ parameter. The authors also analyze anomaly cancellation, potential extensions to higher dimensions (notably 6D with tree-level quartic Higgs terms), and emphasize the need for a thorough phenomenological study of localized terms and heavy bulk fields to assess viability.

Abstract

We study higher-dimensional non-supersymmetric orbifold models where the Higgs field is identified with some internal component of a gauge field. We address two important and related issues that constitute severe obstacles towards model building within this type of constructions: the possibilities of achieving satisfactory Yukawa couplings and Higgs potentials. We consider models where matter fermions are localized at the orbifold fixed-points and couple to additional heavy fermions in the bulk. When integrated out, the latter induce tree-level non-local Yukawa interactions and a quantum contribution to the Higgs potential that we explicitly evaluate and analyse. The general features of these highly constrained models are illustrated through a minimal but potentially realistic five-dimensional example. Finally, we discuss possible cures for the persisting difficulties in achieving acceptable top and Higgs masses. In particular, we consider in some detail the effects induced in these models by adding localized kinetic terms for gauge fields.

Figures (3)

• Figure 1: Different contributions to the effective potential (in arbitrary units): the bulk and boundary fermion contributions (upper left) and the full potential (upper right) for $\lambda=1.57$, $\epsilon_1=3.1$, $\epsilon_2=0.7$ and $\delta = 0$; the bulk and boundary fermion contributions (lower left) and the full potential (lower right) for $\lambda=1.83$, $\epsilon_1=6.4$, $\epsilon_2=6.1$ and $\delta = 1$.
• Figure 2: The full effective potential (in arbitrary units) in the presence of high-rank bulk fermions. Left: $r=8$, $\lambda=3.47$, $\epsilon_1=\epsilon_2=9$ and $\delta=0$, resulting in $m_H=112$ GeV and $1/R=830$ GeV. Right: $r=6$, $\lambda=2.23$, $\epsilon_1=7$, $\epsilon_2=1$ and $\delta=1$, resulting in $m_H=104$ GeV and $1/R=600$ GeV.
• Figure 3: Gauge contribution to the effective potential (in arbitrary units) in the presence of localized gauge kinetic terms, with $c_{2}=0$ and increasing values of $c_1$.