Fun with Higgsless Theories

TL;DR

The paper analyzes Higgsless theories realized through deconstruction of an extra dimension, focusing on an $SU(2)_0\times SU(2)^N\times U(1)$ gauge structure with arbitrary custodial-symmetric breaking. It develops a strong-coupling expansion in the extra gauge couplings $g_j$ and a mechanical analog of masses and springs to interpret the $W$ and $Z$ mass matrices and the electroweak parameters, especially the $S$ parameter. The main finding is that, in this broad class, one cannot raise the light scalar (Higgs) mass without affecting $S$—the low-energy $W$ and $Z$ phenomenology remains SM-like only in a delicate limit, and increasing the Higgs scale tends to increase $S$. This provides a robust, physically intuitive constraint on Higgsless scenarios and highlights the tension between elevating the Higgs mass and keeping electroweak precision data consistent, as illustrated by the spring-mass analogy.

Abstract

Motivated by recent works on ``Higgsless theories,'' I discuss an $SU(2)_0\times SU(2)^{N}\times U(1)$ gauge theory with arbitrary bifundamental (or custodial SU(2) preserving) symmetry breaking between the gauge subgroups and with ordinary matter transforming only under the U(1) and $SU(2)_0$. When the couplings, $g_j$, of the other SU(2)s are very large, this reproduces the standard model at the tree level. I calculate the $W$ and $Z$ masses and other electroweak parameters in a perturbative expansion in $1/g_j^2$, and give physical interpretations of the results in a mechanical analog built out of masses and springs. In the mechanical analog, it is clear that even for arbitrary patterns of symmetry breaking, it is not possible (in the perturbative regime) to raise the Higgs mass by a large factor while keeping the $S$ parameter small.

Figures (5)

• Figure 1: The Moose diagram associated with the linear model.
• Figure 2: The three "non-linear" (meaning not equivalent to the linear model) symmetry breaking patterns for $N=1$.
• Figure 3: A Moose diagram for general symmetry breaking for $N=2$. There are fourteen other distinct possibilities (counting the linear model) in which some of the links are missing.
• Figure 4: The mechanical analog of the system in figure \ref{['fig-1']}.
• Figure 5: The mechanical analog for the charged gauge boson mass matrix.