[1] In order to produce quark and lepton masses, technicolor or composite Higgs models have to be "extended" by additional gauge interactions.
Particularly when modelled on QCD, extended technicolor was challenged by experimental constraints on flavor-changing neutral current and precision electroweak measurements.
A particularly active framework is "walking" technicolor, which exhibits nearly conformal behavior caused by an infrared fixed point with strength just above that necessary for spontaneous chiral symmetry breaking.
[2] Experiments at the Large Hadron Collider have discovered the mechanism responsible for electroweak symmetry breaking, i.e., the Higgs boson, with mass approximately 125 GeV/c2;[3][4][5] such a particle is not generically predicted by technicolor models.
[6] Composite Higgs models are generally solved by the top quark infrared fixed point, and may require a new dynamics at extremely high energies such as topcolor.
The simplest mechanism of electroweak symmetry breaking introduces a single complex field and predicts the existence of the Higgs boson.
Typically, the Higgs boson is "unnatural" in the sense that quantum mechanical fluctuations produce corrections to its mass that lift it to such high values that it cannot play the role for which it was introduced.
These strong forces spontaneously break the massless fermions' chiral symmetries, some of which are weakly gauged as part of the Standard Model.
The new strong interaction leads to a host of new composite, short-lived particles at energies accessible at the Large Hadron Collider (LHC).
Based on analogy with quantum chromodynamics (QCD), it is assumed that there are one or more doublets of massless Dirac "technifermions" transforming vectorially under the same complex representation of GTC,
Continuing the analogy with QCD, the running gauge coupling αTC(μ) triggers spontaneous chiral symmetry breaking, the technifermions acquire a dynamical mass, and a number of massless Goldstone bosons result.
If the technifermions transform under [SU(2) ⊗ U(1)]EW as left-handed doublets and right-handed singlets, three linear combinations of these Goldstone bosons couple to three of the electroweak gauge currents.
In the Standard Model, quarks and leptons are necessarily massless because they transform under SU(2) ⊗ U(1) as left-handed doublets and right-handed singlets.
(In general, electroweak-eigenstate fermions are not mass eigenstates, so this process also induces the mixing matrices observed in charged-current weak interactions.)
The picture, then, is that there is a large "extended technicolor" (ETC) gauge group GETC ⊃ GTC in which technifermions, quarks, and leptons live in the same representations.
[clarification needed] Extended technicolor is a very ambitious proposal, requiring that quark and lepton masses and mixing angles arise from experimentally accessible interactions.
In 1981 Holdom suggested that, if the αTC(μ) evolves to a nontrivial fixed point in the ultraviolet, with a large positive anomalous dimension γm for
In 1986 Akiba and Yanagida also considered enhancing quark and lepton masses, by simply assuming that αTC is constant and strong all the way up to the ETC scale.
[18] In the same year Yamawaki, Bando, and Matumoto again imagined an ultraviolet fixed point in a non-asymptotically free theory to enhance the technifermion condensate.
[19] In 1986 Appelquist, Karabali and Wijewardhana discussed the enhancement of fermion masses in an asymptotically free technicolor theory with a slowly running, or "walking", gauge coupling.
[21] They took the analysis to three loops, noted that the walking can lead to a power law enhancement of the technifermion condensate, and estimated the resultant quark, lepton, and technipion masses.
[22] In the 1990s, the idea emerged more clearly that walking is naturally described by asymptotically free gauge theories dominated in the infrared by an approximate fixed point.
Below some critical value Nfc the coupling becomes strong enough (> αχ SB) to break spontaneously the massless technifermions' chiral symmetry.
Since the analysis must typically go beyond two-loop perturbation theory, the definition of the running coupling αTC(μ), its fixed point value αIR, and the strength αχ SB necessary for chiral symmetry breaking depend on the particular renormalization scheme adopted.
; i.e., for Nf just below Nfc, the evolution of αTC(μ) is governed by the infrared fixed point and it will evolve slowly (walk) for a range of momenta above the breaking scale ΛTC.
The idea that αTC(μ) walks for a large range of momenta when αIR lies just above αχ SB was suggested by Lane and Ramana.
[26] Combining a perturbative computation of the infrared fixed point with an approximation of αχ SB based on the Schwinger–Dyson equation, they estimated the critical value Nfc and explored the resultant electroweak physics.
The enhancement described above for walking technicolor may not be sufficient to generate the measured top quark mass, even for an ETC scale as low as a few TeV.
[46][47] The Peskin–Takeuchi analysis was based on the general formalism for weak radiative corrections developed by Kennedy, Lynn, Peskin and Stuart,[48] and alternate formulations also exist.
[62] An April 2011 announcement of an excess in jet pairs produced in association with a W boson measured at the Tevatron[63] has been interpreted by Eichten, Lane and Martin as a possible signal of the technipion of low-scale technicolor.