These scenarios are models for physics beyond the SM presently tested at the Large Hadron Collider (LHC) in Geneva.
This dimension may be related to the Fermi scale (100 GeV) that determines the strength of the weak interactions such as in β-decay, but it could be significantly smaller.
This was described by Yoichiro Nambu and subsequently developed by Miransky, Tanabashi, and Yamawaki [3][4] and Bardeen, Hill, and Lindner,[5] who connected the theory to the renormalization group and improved its predictions.
A more recent version of the Top Seesaw model of Dobrescu and Cheng has an acceptable light composite Higgs boson.
Within the most compelling scenarios each Standard Model particle has a partner with equal quantum numbers but heavier mass.
For example, the photon, W and Z bosons have heavy replicas with mass determined by the compositeness scale, expected around 1 TeV.
From the LHC discovery of 2012, it is known that there exists a physical Higgs boson (a weak iso-doublet) that condenses to break the electro-weak symmetry.
This differs from the prediction ordinary technicolor theories where new strong dynamics directly breaks the electro-weak symmetry without the need of a physical Higgs boson.
The CHM proposed by Georgi and Kaplan was based on known gauge theory dynamics that produces the Higgs doublet as a Goldstone boson.
It was later realized, as with the case of Top Seesaw models described above, that this can naturally arise in five-dimensional theories, such as the Randall–Sundrum scenario or by dimensional deconstruction.
These scenarios can also be realized in hypothetical strongly coupled conformal field theories (CFT) and the AdS-CFT correspondence.
Detailed phenomenological studies showed that within this framework agreement with experimental data can be obtained with a mild tuning of parameters.
Broadly they can be divided in two categories: In both cases the electro-weak symmetry is broken by the condensation of a Higgs scalar doublet.
In the first type of scenario there is no a priori reason why the Higgs boson is lighter than the other composite states and moreover larger deviations from the SM are expected.
It is assumed that the composite sector has a global symmetry G spontaneously broken to a subgroup H where G and H are compact Lie groups.
By appropriately choosing the global symmetries it is possible to have Goldstone bosons that correspond to the Higgs doublet in the SM.
For example, for the model above with SO(5) global symmetry the coupling of the Higgs to W and Z bosons is modified as Phenomenological studies suggest f > 1 TeV and thus at least a factor of a few larger than v .
Minimally these are the SM Yukawa and gauge couplings that cannot respect the global symmetry but other effects can also exist.
For example, a strongly motivated representation for left-handed fermions is the (2,2) that contains particles with exotic electric charge ++5/3 or –+4/3 with special experimental signatures.
After the first run of the LHC the couplings of the Higgs with fermions and gauge bosons agree with the SM with a precision around 20%.
The hypothesis of partial compositeness allows to suppress flavor violation beyond the SM that is severely constrained experimentally.
The fact that nature provides a single (weak isodoublet) scalar field that ostensibly uniquely generates fundamental particle masses has yet to be explained.
At present, we have no idea what mass / energy scale will reveal additional information about the Higgs boson that may shed useful light on these issues.
While theorists remain busy concocting explanations, this limited insight poses a major challenge to experimental particle physics: We have no clear idea whether feasible accelerators might provide new useful information beyond the S.M.