Standard Model Higgs from Higher Dimensional Gauge Fields

TL;DR

The paper proposes that the SM Higgs may originate as an extra-dimensional component of a higher-dimensional gauge field in a 6D $G_2$ theory compactified on $T^2/Z_4$, yielding the SM bosonic content and a tree-level prediction $\\\sin^2\theta_W=1/4$. The Higgs quartic is generated by the 6D gauge interaction, predicting a light Higgs, while potential brane-induced tadpoles are carefully analyzed and shown to be absent at one loop for the viable $Z_4$ setup. Fermions are placed at orbifold fixed points and Yukawa couplings arise from non-local Wilson-line operators, with hierarchies achievable by integrating out bulk fermions; the top sector can trigger electroweak symmetry breaking via radiative corrections. The analysis finds a TeV-scale spectrum with first KK modes and extra localized fermions, and a cutoff at a few tens of TeV, providing a testable framework for Higgs physics that embeds electroweak breaking into higher-dimensional gauge dynamics.

Abstract

We consider the possibility that the standard model Higgs fields may originate from extra components of higher dimensional gauge fields. Theories of this type considered before have had problems accommodating the standard model fermion content and Yukawa couplings different from the gauge coupling. Considering orbifolds based on abelian discrete groups we are lead to a 6 dimensional G_2 gauge theory compactified on T^2/Z_4. This theory can naturally produce the SM Higgs fields with the right quantum numbers while predicting the value of the weak mixing angle sin^2 theta_W = 0.25 at the tree-level, close to the experimentally observed one. The quartic scalar coupling for the Higgs is generated by the higher dimensional gauge interaction and predicts the existence of a light Higgs. We point out that one can write a quadratically divergent counter term for Higgs mass localized to the orbifold fixed point. However, we calculate these operators and show that higher dimensional gauge interactions do not generate them at least at one loop. Fermions are introduced at orbifold fixed points, making it easy to accommodate the standard model fermion content. Yukawa interactions are generated by Wilson lines. They may be generated by the exchange of massive bulk fermions, and the fermion mass hierarchy can be obtained. Around a TeV, the first KK modes would appear as well as additional fermion modes localized at the fixed point needed to cancel the quadratic divergences from the Yukawa interactions. The cutoff scale of the theory could be a few times 10 TeV.

Figures (3)

• Figure 1: Symmetries of the orbifold. $T$ corresponds to torus identification while $O$ is the action of the orbifold symmetry. The fundamental domain of the orbifold space-time is the square $\pi R\times \pi R$ (however, for convenience, we will still normalize the KK modes by integration over the fundamental domain of the torus). Two points are left invariant by the orbifold action: the origin, $(0,0)$, and the point $(\pi R,\pi R)$. At these points, the $G_2$ gauge group of the bulk is broken to $SU(2)\times U(1)$ and gauge invariant potentially dangerous operators could be in principle generated
• Figure 2: The gauge and ghost contributions to the tadpole in operator (\ref{['badguy']}).
• Figure 3: Radiative corrections, from Yukawa interactions, to the SM Higgs square mass, $m_h^2$, and to the $3/2$ hypercharge Higgs square mass, $m_H^2$.