Top quark condensate

The top quark condensate theory was an alternative to the Standard Model in which a fundamental scalar Higgs field is replaced by a composite field composed of the top quark and its antiquark. The top quark is chosen because it is the most massive among all quarks (its mass 173GeV is comparable to the electroweak scale).

In representation theory, a quark is described by a Dirac spinor, which can be thought of as a pair of Weyl spinors describing the left-handed (negative helicity) and the right-handed (positive helicity) quark.

The following paragraph describes the representations of the Standard Model group in which the relevant fields transform.

Forming the condensate are:

• The left-handed top quark, belonging to a $(3,2)_{1 \over 6}$ representation
• The left-handed antitop antiquark, belonging to $({\bar {3}},1)_{-{2 \over 3}}$ representation

In these groups, the left number refers to SU(3) of Quantum chromodynamics, whereas the second denotes the representation under SU(2). The subscript labels the hypercharge.

The top and antitop quark form a bound state described by a $(1,2)_{-{1 \over 2}}$ composite scalar field, which forms a fermion condensate, which subsequently breaks the electroweak and hypercharge symmetry into electromagnetism.

This model correctly predicts that the electroweak scale matches the top quark mass. However, to be natural (i.e. to stabilize the Higgs mass squared from quadratically divergent radiative corrections) it requires new physics at a relatively low scale. Placing new physics at 10 TeV, for instance, the model incorrectly predicts that the top is significantly heavier than observed (about 600 GeV). So-called "top seesaw" models attempt to get around this difficulty. If the new physics does not occur until the GUT scale, the predicted top mass is approximately correct, but the theory is very fine-tuned.

The model was proposed by Miransky, Tanabashi, Yamawaki, and Nambu. In 1991, Anna Hasenfratz and Peter Hasenfratz et al. demonstrated the model is approximately equivalent to a fundamental Higgs scalar field. This equivalence is exact in the limit of the large number of colors (if we disregard the irrelevant terms suppressed by the cutoff scale (the scale at which new physics appears)). However, even for a finite number of colors, it has been shown that new predictions cannot be derived from a top quark condensate (if the cutoff scale is high).

See also

• fermion condensate
• technicolor (physics)
• Hierarchy problem