On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

18 Chapter 1. Introduction: Problems beyond the Standard Model
SU(2)L × U(1)Y
breaking vacuum
v
θ
R = f
SU(2)L × U(1)Y
preserving vacuum
Figure 1.5: Circle of a priori degenerate minima in Composite Higgs models with
radius R = f, the scale at which the global theory is broken and the Higgs emerges
as a pseudo Nambu-Goldstone boson. The angle θ measures the (mis-)alignment with
the EWSB vacuum.
contribution to the potential reintroduces a tension comparable to the situation of
higgsless TC models, consult [61, Sec.3.4] for details.
In terms of the angle sin θ, it also becomes clear how composite Higgs models can be
seen as a link between the SM with an elementary Higgs scalar and TC theories. If
f → ∞, sin θ → 0 and all composite states besides the Higgs decouple, so that the
theory effectively has an elementary Higgs. For v → f however, sin θ → 1 and the
model predicts only a single characteristic scale, at which the composites form and
EWSB occurs, just like TC.
Collective Symmetry Breaking
In composite Higgs models one can achieve a natural separation of scales v < f,
but the Higgs mass does still encounter quadratically divergent corrections up to the
compositeness scale, because gauge and Yukawa interactions explicitly break the shift
symmetry which protects it. Therefore, a large separation v ≪ f is unnatural. Loosely
speaking, one could say that the Higgs does not profit from being a Nambu Goldstone
boson.
This was the inspiration for the mechanism of collective symmetry breaking, which is
realized in a class of models called little Higgs [38]. 17 The idea is, that the global
symmetry, which breaks dynamically in the composite Higgs model is larger than
necessary in order to accommodate the four Goldstone bosons which are identified
with the degrees of freedom of the Higgs, and the electroweak gauge group is enlarged
as well, so that there is at least another copy of W ± s and the Z, which becomes heavy
by eating the additional GBs.
17 The name is motivated, because the Higgs in these models is naturally light = little. See Section
1.3 in [38].