The idea was described by Yoichiro Nambu and subsequently developed by Miransky, Tanabashi, and Yamawaki and Bardeen, Hill, and Lindner, who connected the theory to the renormalization group, and improved its predictions. The renormalization group reveals that top quark condensation is fundamentally based upon the ‘infrared fixed point’ for the top quark Higgs-Yukawa coupling, proposed by Pendleton and Ross. and Hill, The ‘infrared’ fixed point originally predicted that the top quark would be heavy, contrary to the prevailing view of the early 1980s. Indeed, the top quark was discovered in 1995 at the large mass of 175 GeV. The infrared-fixed point implies that it is strongly coupled to the Higgs boson at very high energies, corresponding to the Landau pole of the Higgs-Yukawa coupling. At this high scale a bound-state Higgs forms, and in the ‘infrared’, the coupling relaxes to its measured value of order unity by the renormalization group. The Standard Model renormalization group fixed point prediction is about 220 GeV, and roughly 25% higher than the observed top mass. The simplest top condensation models also predicted that the Higgs boson mass would be about 250 GeV, and have now been ruled out by the LHC discovery of the Higgs boson at a mass scale of 125 GeV. However, extended versions of the theory, introducing more particles, can be made consistent with the observed top quark mass.
Future
The composite Higgs boson arises naturally in Topcolor models, that are extensions of the standard model using a new force analogous to quantum chromodynamics. To be natural, without excessive fine-tuning, 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. Top Seesaw models, also based upon Topcolor, circumvent this difficulty. The predicted top quark mass comes into improved agreement with the fixed point if there are many additional Higgs scalars beyond the standard model. This may be indicating a rich spectroscopy of new composite Higgs fields at energy scales that can be probed with the LHC and its upgrades. The general idea of a composite Higgs boson, connected in a fundamental way to the top quark, remains compelling, though the full details are not yet understood.
