Electroweak Symmetry Breaking and Extra Dimensions

TL;DR

This work proposes a dynamical mechanism for electroweak symmetry breaking in a higher-dimensional setting where no fundamental Higgs exists below the quantum gravity scale $M_s$. Electroweak breaking is driven by QCD in compact extra dimensions, which generate four-quark operators via KK-gluon exchange and bind a composite Higgs doublet from the left-handed top-bottom doublet and the KK tower of the right-handed top quark, leaving the low-energy theory as the Standard Model with a Higgs sector arising from strong dynamics. The top quark mass is controlled by the number of active $t_R$ KK modes, yielding $m_t \\sim 600~ ext{GeV}/\\sqrt{n_{ m KK}}$ and indicating $n_{ m KK} \\approx 12$ to match experiment, while the Higgs sector can be heavy or moderately light depending on the localization of fields and mixing with additional composites. The framework ties electroweak breaking to TeV-scale extra dimensions, predicts TeV-scale KK states (including KK gluons) that modify precision observables and collider signatures, and provides a natural arena where a composite Higgs emerges without introducing new fundamental scalars below $M_s$.

Abstract

Electroweak symmetry can be naturally broken by observed quark and gauge fields in various extra-dimensional configurations. No new {\it fundamental} fields are required below the quantum gravitational scale ($\sim$ 10 - 100 TeV). We examine schemes in which the QCD gauge group alone, in compact extra dimensions, forms a composite Higgs doublet out of (t,b)_L and a linear combination of the Kaluza-Klein modes of t_R. The effective theory at low energies is the Standard Model. The top-quark mass is controlled by the number of active t_R Kaluza-Klein modes below the string scale, and is in agreement with experiment.

Figures (3)

• Figure 1: The profile of the compact space. The $x$-coordinates of the flat three-dimensional space are transverse to the plane of the page. The $z_1, ..., z_{\delta - 1}$ coordinates are depicted collectively as one axis. The gluons propagate inside the rectangle, the $\chi$ propagates along the $y$ axis, on the thick line, and the $\psi_L$ is located at the point marked on the $y$ axis.
• Figure 2: Large-$N_c$ contributions to the composite scalar self-energies. The vertical lines are four dimensional fields localized at $y = y_0$, and the curved or slanted lines are five-dimensional fields. The external lines represent the $H$ and $\varphi$, while in the loops run the $\psi_L$ and $\chi$ quarks.
• Figure 3: Large-$N_c$ contributions to the $\tilde{\lambda}_H, \tilde{\lambda}_0$ and $\tilde{\lambda}_\varphi$ quartic couplings. The lines represent fields as explained in the caption of Fig. 2.