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. More recently, the model was shown to be equivalent to the standard fundamental Higgs boson.

The detailed mathematical structure of the composite field requires one to discuss representation theory. A quark is described by a Dirac spinor that can be thought of as a pair of Weyl spinors describing the left-handed and the right-handed quark. The following paragraph describes the representations of the Standard Model group in which the relevant fields transform. The first number in the parentheses refers to SU(3) of Quantum Chromodynamics, the second number denotes the representation under SU(2). The subscript will label the hypercharge.

The left handed top quark belongs to a $(3,2)_{1 \over 6}$ representation wheareas the left handed antitop antiquark belongs to a $({\bar {3}},1)_{-{2 \over 3}}$ representation. The top and antitop quark forms a bound state described by a $(1,2)_{-{1 \over 2}}$ composite scalar field. This composite field forms a condensate, leading to a fermion condensate which spontaneously breaks the electroweak and hypercharge symmetry into electromagnetism.

This model predicts that the electroweak scale matches the top quark mass, which it does.

In this theory is there is no problem of stabilizing the Higgs mass squared from quadratically divergent radiative corrections (see Hierarchy problem), and thus, no need for supersymmetry.

The model was proposed by Miransky, Tanabashi and Yamawaki (MTY) and by Nambu. Anna Hasenfratz et al. have proved in 1991 that the model is approximately equivalent to a fundamental Higgs scalar field. The equivalence is exact in the limit of the large number of colors but even for a finite number of colors, it has been shown that no new predictions can be derived from the top quark condensate.

See also fermion condensate, technicolor (physics)