User:Jarcanist/Quark

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 quark.

A quark is described by a Dirac spinor that can be thought of as a pair of Weyl spinors describing the left-handed (that is to say, it has 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.

In Quantum chromodynamics, the notation (for example) $$(1,2)_{-{1\over 2}}$$ is used to describe a bound state. In this case, the first number, 1, refers to SU(3) (a special unitary group, referring to the rotation group), whereas the second number, 2, refers to SU(2) (which is the group of complex unitary 2×2 matrices of determinant 1). The subscript labels 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, Yamawaki, and Nambu. In 1991, Anna 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. However, even for a finite number of colors, it has been shown that new predictions cannot be derived from a top quark condensate.