Technicolor theories are models of physics beyond the Standard Model that address electroweak gauge symmetry breaking, the mechanism through which W and Z bosons acquire masses. Early technicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of the strong nuclear force, which inspired their name.
Instead of introducing elementary Higgs bosons to explain observed phenomena, technicolor models were introduced to dynamically generate masses for the W and Z bosons through new gauge interactions. Although asymptotically free at very high energies, these interactions must become strong and confining (and hence unobservable) at lower energies that have been experimentally probed. This dynamical approach is natural and avoids issues of quantum triviality and the hierarchy problem of the Standard Model.
However, the original models are largely ruled out since experiments in 2012 at CERN's Large Hadron Collider have discovered the mechanism responsible for electroweak symmetry breaking, i.e., the Higgs boson, with mass approximately ; such a particle is not generically predicted by technicolor models. Nonetheless, it remains a possibility that the Higgs boson is a composite state,For introductions to and reviews of technicolor and strong dynamics, see the following: e.g., built of top and anti-top quarks as in the Bardeen–Hill–Lindner theory.. 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.
In order to produce quark and lepton masses, technicolor or composite Higgs models (CHM) 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. The specific extensions of particle dynamics for technicolor or composite Higgs bosons are unknown.
Much technicolor research focuses on exploring strongly interacting gauge theories other than QCD, in order to evade some of these challenges. 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. Whether walking can occur and lead to agreement with precision electroweak measurements is being studied through non-perturbative lattice simulations.
Introduction The mechanism for the breaking of electroweak gauge symmetry in the Standard Model of elementary particle interactions remains unknown. The breaking must be spontaneous, meaning that the underlying theory manifests the symmetry exactly (the gauge-boson fields are massless in the equations of motion), but the solutions (the ground state and the excited states) do not. In particular, the physical W and Z gauge bosons become massive. This phenomenon, in which the W and Z bosons also acquire an extra polarization state, is called the "Higgs mechanism". Despite the precise agreement of the electroweak theory with experiment at energies accessible so far, the necessary ingredients for the symmetry breaking remain hidden, yet to be revealed at higher energies.
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. Unless the Standard Model breaks down at energies less than a few TeV, the Higgs mass can be kept small only by a delicate fine-tuning of parameters.
Technicolor avoids this problem by hypothesizing a new gauge interaction coupled to new massless fermions. This interaction is asymptotically free at very high energies and becomes strong and confining as the energy decreases to the electroweak scale of 246 GeV. These strong forces spontaneously break the massless fermions' chiral symmetries, some of which are weakly gauged as part of the Standard Model. This is the dynamical version of the Higgs mechanism. The electroweak gauge symmetry is thus broken, producing masses for the W and Z bosons.
The new strong interaction leads to a host of new composite, short-lived particles at energies accessible at the Large Hadron Collider (LHC). This framework is natural because there are no elementary Higgs bosons and, hence, no fine-tuning of parameters. Quark and lepton masses also break the electroweak gauge symmetries, so they, too, must arise spontaneously. A mechanism for incorporating this feature is known as extended technicolor. Technicolor and extended technicolor face a number of phenomenological challenges, in particular issues of flavor-changing neutral currents, precision electroweak tests, and the top quark mass. Technicolor models also do not generically predict Higgs-like bosons as light as ; such a particle was discovered by experiments at the Large Hadron Collider in 2012. Some of these issues can be addressed with a class of theories known as "walking technicolor".
Early technicolor Technicolor is the name given to the theory of electroweak symmetry breaking by new strong gauge-interactions whose characteristic energy scale is the weak scale itself, . The guiding principle of technicolor is "naturalness": basic physical phenomena should not require fine-tuning of the parameters in the Lagrangian that describes them. What constitutes fine-tuning is to some extent a subjective matter, but a theory with elementary scalar particles typically is very finely tuned (unless it is supersymmetric). The quadratic divergence in the scalar's mass requires adjustments of a part in , where bare is the cutoff of the theory, the energy scale at which the theory changes in some essential way. In the standard electroweak model with (the grand-unification mass scale), and with the Higgs boson mass , the mass is tuned to at least a part in 10.
By contrast, a natural theory of electroweak symmetry breaking is an asymptotically free gauge theory with fermions as the only matter fields. The technicolor gauge group G is often assumed to be SU(). 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 G, . Thus, there is a chiral symmetry of these fermions, e.g., , if they all transform according to the same complex representation of G. Continuing the analogy with QCD, the running gauge coupling () triggers spontaneous chiral symmetry breaking, the technifermions acquire a dynamical mass, and a number of massless Goldstone bosons result. If the technifermions transform under as left-handed doublets and right-handed singlets, three linear combinations of these Goldstone bosons couple to three of the electroweak gauge currents.
In 1973 Jackiw and Johnson and Cornwall and Norton studied the possibility that a (non-vectorial) gauge interaction of fermions can break itself; i.e., is strong enough to form a Goldstone boson coupled to the gauge current. Using Abelian gauge models, they showed that, if such a Goldstone boson is formed, it is "eaten" by the Higgs mechanism, becoming the longitudinal component of the now massive gauge boson. Technically, the polarization function () appearing in the gauge boson propagator,
develops a pole at with residue , the square of the Goldstone boson's decay constant, and the gauge boson acquires mass . In 1973, Weinstein showed that composite Goldstone bosons whose constituent fermions transform in the "standard" way under SU(2) ⊗ U(1) generate the weak boson masses
This standard-model relation is achieved with elementary Higgs bosons in electroweak doublets; it is verified experimentally to better than 1%. Here, and are SU(2) and U(1) gauge couplings and defines the weak mixing angle.
The important idea of a new strong gauge interaction of massless fermions at the electroweak scale driving the spontaneous breakdown of its global chiral symmetry, of which an SU(2) ⊗ U(1) subgroup is weakly gauged, was first proposed in 1979 by Weinberg. This "technicolor" mechanism is natural in that no fine-tuning of parameters is necessary.
Extended technicolor Elementary Higgs bosons perform another important task. In the Standard Model, quarks and leptons are necessarily massless because they transform under as left-handed doublets and right-handed singlets. The Higgs doublet couples to these fermions. When it develops its vacuum expectation value, it transmits this electroweak breaking to the quarks and leptons, giving them their observed masses. (In general, electroweak-eigenstate fermions are not mass eigenstates, so this process also induces the mixing matrices observed in charged-current weak interactions.)
In technicolor, something else must generate the quark and lepton masses. The only natural possibility, one avoiding the introduction of elementary scalars, is to enlarge TC to allow technifermions to couple to quarks and leptons. This coupling is induced by gauge bosons of the enlarged group. The picture, then, is that there is a large "extended technicolor" (ETC) gauge group in which technifermions, quarks, and leptons live in the same representations. At one or more high scales ETC, ETC is broken down to TC, and quarks and leptons emerge as the TC-singlet fermions. When TC() becomes strong at scale TC ≈ EW, the fermionic condensate forms. (The condensate is the vacuum expectation value of the technifermion bilinear . The estimate here is based on naive dimensional analysis of the quark condensate in QCD, expected to be correct as an order of magnitude.) Then, the transitions can proceed through the technifermion's dynamical mass by the emission and reabsorption of ETC bosons whose masses ETC ≈ ETC ETC are much greater than TC. The quarks and leptons develop masses given approximately by
Here, is the technifermion condensate renormalized at the ETC boson mass scale,
where m() is the anomalous dimension of the technifermion bilinear at the scale . The second estimate in Eq. (2) depends on the assumption that, as happens in QCD, TC() becomes weak not far above TC, so that the anomalous dimension m of is small there. Extended technicolor was introduced in 1979 by Dimopoulos and Susskind, and by Eichten and Lane. For a quark of mass ≈ 1 GeV, and with TC ≈ 246 GeV, one estimates ETC ≈ 15 TeV. Therefore, assuming that , ETC will be at least this large.
In addition to the ETC proposal for quark and lepton masses, Eichten and Lane observed that the size of the ETC representations required to generate all quark and lepton masses suggests that there will be more than one electroweak doublet of technifermions. If so, there will be more (spontaneously broken) chiral symmetries and therefore more Goldstone bosons than are eaten by the Higgs mechanism. These must acquire mass by virtue of the fact that the extra chiral symmetries are also explicitly broken, by the standard-model interactions and the ETC interactions. These "pseudo-Goldstone bosons" are called technipions, T. An application of Dashen's theorem gives for the ETC contribution to their mass
The second approximation in Eq. (4) assumes that . For EW ≈ TC ≈ 246 GeV and ETC ≈ 15 TeV, this contribution to T is about 50 GeV. Since ETC interactions generate and the coupling of technipions to quark and lepton pairs, one expects the couplings to be Higgs-like; i.e., roughly proportional to the masses of the quarks and leptons. This means that technipions are expected to predominately decay to the heaviest possible and pairs.