# Technicolor

# TECHNICOLOR

The discovery of the *W* and *Z* bosons in 1983 at the European Laboratory for Particle Physics (CERN) in Geneva, Switzerland, provided compelling evidence that the electroweak theory proposed by Sheldon Glashow, Abdus Salam, and Stephen Weinberg was an excellent description of both electromagnetic and weak interactions. By that time it had become a central part of what was known as the Standard Model of particle physics, and Glashow, Salam, and Weinberg (GSW) had already been awarded the 1979 Nobel Prize in Physics for their electroweak theory. In spite of this success, particle theorists were eager to determine whether a more fundamental theory could be behind the GSW model.

## Electroweak Symmetry Breaking

A key ingredient of the GSW electroweak theory is the mechanism that forces the vacuum to distinguish the *W* and *Z* from the photon (breaking the symmetry of the electroweak gauge interactions), giving masses to the former while keeping the latter exactly massless. This symmetry breaking goes by the name Higgs mechanism. In addition to fields corresponding to the spin-1 gauge bosons (force carriers), it is necessary to add another boson field with zero spin, called the Higgs field, which has the peculiar property of a nonzero probability to measure the Higgs field in a pure vacuum. It may be helpful to recall the situation that arises in superconductors since this provides a relatively simple analogy. In a superconductor, electrons can attract each other (very weakly) by exchanging phonons (quanta of lattice vibrations) forming Cooper pairs. If the charged Cooper pairs undergo Bose condensation, the lowest energy state of the system has an arbitrarily large charge (limited only by the size of the superconductor). Photons moving through this charged medium are effectively massive, as can be seen by the fact that magnetic fields cannot penetrate a super-conductor. In the analogy with the GSW electroweak theory, the analog of the Cooper pair is the Higgs field, the analog of the lowest-energy state is the vacuum of space-time, and the analogs of the massive photon are the massive *W* and *Z.*

In the GSW electroweak theory, the Higgs field has an electroweak charge, and the theory is arranged so that in empty space there is a nonzero probability to measure the Higgs field (this is the analog of Bose condensation). Allowing the Higgs field to couple to fermions (particles with spin ½) also gives masses to the quarks and leptons. This relatively simple set of ideas leads to a prediction of the ratio of *W* and *Z* masses that was confirmed by experiment. During the 1990s the GSW electroweak theory was subjected to precision tests by experiments at the Stanford Linear Accelerator and at CERN. In order to accurately compare the theory to experiment, quantum corrections to the predictions had to be included. In fact, many particle theorists believed that the GSW electroweak theory was not self-consistent until an understanding of how to perform such quantum corrections had been developed in the early 1970s by Gerardus 't Hooft and Martinus Veltmann. GSW electroweak theory was confirmed at better than the 1 percent level, and 't Hooft and Veltmann won the 1999 Nobel Prize in Physics.

## Fine-tuning

In spite of the great successes of the GSW electroweak theory, particle theorists began to suspect as early as the 1970s that it could not be the whole story. The reason was that although 't Hooft and Veltmann had shown how to calculate the quantum corrections to the theory, some of these corrections were extremely sensitive to the highest possible energy scales, and as a consequence, the parameters of the theory had to be fine-tuned to many decimal places. To see how this arises, one can look at the quantum corrections to the propagation of the Higgs boson. For GSW electroweak theory to be consistent, the Higgs boson mass must be below 1,000 GeV/*c*^{2}. Consider, for example, how the coupling of the Higgs to the top quark leads to an extremely large correction to the Higgs mass. This coupling allows a single Higgs boson moving through space to turn into (for a short amount of time governed by Heisenberg's uncertainty principle) a top quark and an antitop quark; the top and antitop quickly recombine to again form a single Higgs boson. (A diagram of the trajectory of the quarks in space-time looks like a closed loop, and this type of correction is called a quantum loop correction.) Quantum mechanics requires that if the intermediate state of the system (the top-antitop pair) is not measured, all possibilities must be summed over in order to calculate that probability amplitude. The sum of the energy and momentum of the top-antitop pair must, of course, add up to the original energy and momentum of the single Higgs, but the differences in energy and momentum of the top and the antitop are unconstrained.

Since energy and momentum are continuous quantities, one has to integrate over these variables. The amplitudes for top-antitop propagation are such that the integrals diverge; that is, if it is assumed there is some maximum amount of energy that the intermediate top and antitop quarks can have, then the integral is proportional to the square of this energy cut-off. This integral gives a direct contribution to the square of the mass of the Higgs boson. If one imagines that the energy cut-off is associated somehow with the scale of gravity (i.e., the Planck scale that is 10^{19} GeV/*c* 2), then the correction to the square of the Higgs mass is about 10^{32} times larger than the answer needed. One can obtain a reasonable answer for the Higgs mass, but it requires fine-tuning the parameters of the theory to thirty-two decimal places in order to arrange for a tremendous cancellation that allows the answer to be many orders of magnitude smaller than the individual contributions. There are many such quantum loop corrections to the Higgs boson mass, and considering multiloop corrections makes the situation even worse. It is known that in supersymmetric extensions of the GSW theory there is a cancellation of divergent corrections between particles and their superpartners, but until the origin of electroweak symmetry breaking is uncovered experimentally, other explanations must be considered.

## New Interactions

In the 1970s Stephen Weinberg and Leonard Susskind independently proposed that composite particles formed by a new strong interaction could replace the Higgs boson in GSW theory. The new interactions were supposed to be similar to those of quantum chromodynamics (QCD), and these theories were hence dubbed technicolor theories. Susskind showed that if the Higgs boson was absent from the Standard Model, QCD would provide electroweak symmetry breaking through quark composites (although it would give masses for the *W* and *Z* that are about a factor of 2,600 too small). Techni-color theories thus harkened back to superconductivity where a gauge symmetry is broken by a composite of two fermions, a crucial difference being that the interactions responsible for superconductivity are quite weak, whereas the technicolor interactions must remain strong. Technicolor theories essentially resolve the fine-tuning problem by lowering the effective cut-off scale to 1,000 GeV/*c*^{2}. Remarkably, technicolor theories predicted the correct ratio for the *W* and *Z* masses; however, producing masses for the quarks and leptons requires several complicated extensions of the model. A further problem with technicolor was revealed by the comparison with precision experiments. Following the idea of scaling up QCD to obtain the correct *W* and *Z* masses, it was possible to scale up QCD data (essentially using QCD as an "analog computer") to predict the deviations of a technicolor theory from the GSW theory. These deviations were not seen at SLAC or at CERN. It remains logically possible that there is another version of technicolor that does not behave like QCD, but in the absence of an explicit, workable model interest in technicolor waned during the 1990s.

*See also:*Electroweak Symmetry Breaking; Higgs Phenomenon; Standard Model

## Bibliography

CERN. "Hands on CERN." <http://hands-on-cern.physto.se/hoc_v1en/index.html>.

Dixon, L. "From Superconductors to Supercolliders." <http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-dixon.pdf>.

Nobel e-Museum. "Nobel Laureates in Physics." http://particle adventure.org/particleadventure/index_old.html.

Particle Data Group. "The Particle Adventure." <http://particleadventure.org/particleadventure/index.html>.

SLAC. "SLAC Virtual Visitor Center." <http://www2.slac.stanford.edu/vvc/home.html>.

*John Terning*

# Technicolor

Tech·ni·col·or / ˈtekniˌkələr/ •
n. trademark a process of color cinematography using synchronized monochrome films, each of a different color, to produce a movie in color. ∎ (technicolor) inf. vivid color: [as adj.] *a technicolor bruise.* DERIVATIVES: tech·ni·col·ored adj.

# Technicolor

**Technicolor** Trade name of the colour film process invented by Herbert T. Calmus and Daniel F. Comstock, still used in the majority of motion pictures. A primitive Technicolor first appeared in 1917, and in 1933 Walt Disney used three-colour Technicolor for the animated film Flowers and Trees.

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