# Top quark condensate

In particle physics, the top quark condensate theory is 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. These are bound by a four-fermion interaction, analogous to Cooper pairs in a BCS superconductor and nucleons in the Nambu-Jona-Lasinio model. The top quark condenses because its measured mass is approximately 173 GeV (comparable to the electroweak scale), and so its Yukawa coupling is of order unity, yielding the possibility of strong coupling dynamics.

## Relevant matter content

In group 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 chirality) and the right-handed (positive chirality) quark.

The relevant fields forming the top quark 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.

## History

This model predicts how the electroweak scale may match the top quark mass. The idea was first described by Yoichiro Nambu in a series of talks and then elucidated by Vladimir Miransky, Masaharu Tanabashi, and Koichi Yamawaki in their 1989 paper Is the t Quark Responsible for the Mass of W and Z Bosons?, in which they attempt to set the parameters so that the four-fermion interaction will have an ultraviolet fixed point. A year later it was developed into a more predictive scheme, based upon the renormalization group, by William A. Bardeen, Christopher T. Hill, and Manfred Lindner in the article Minimal Dynamical Symmetry Breaking of the Standard Model in which the authors do not attempt to render the theory renormalizable. Top quark condensation is essentially based upon the "quasi-infrared fixed point" for the top quark Higgs-Yukawa coupling, proposed in 1981 by Hill in the paper Quark and Lepton Masses from Renormalization Group Fixed Points.

In 1991, Anna Hasenfratz and Peter Hasenfratz et al. claimed 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 was claimed that new predictions cannot be derived from a top quark condensate (if the cutoff scale is high). This, however, presumes a bizarre notion of physical compositeness, in which a boundstate could be essentially decoupled from its constituents near its compositeness scale by the effects of superstrong irrelevant operators.

## Generalizations

Top condensation arises naturally in Topcolor models, that are extensions of the standard model in analogy to Quantum Chromodynamics. To be natural, without excessive fine-tuning (i.e. to stabilize the Higgs mass from large radiative corrections), the theory requires new physics at a relatively low energy scale. Placing new physics at 10 TeV, for instance, the model predicts the top quark to be significantly heavier than observed (at about 600 GeV vs. 171 GeV). "Top Seesaw" models, also based upon Topcolor, circumvent this difficulty. These theories will be tested at the LHC.