In physics, an infrared fixed point is a set of coupling constants, or other parameters, that evolve from arbitrary initial values at very high energies (short distance) to fixed, stable values, usually predictable, at low energies (large distance).
[1] This usually involves the use of the renormalization group, which specifically details the way parameters in a physical system (a quantum field theory) depend on the energy scale being probed.
In the statistical physics of second order phase transitions, the physical system approaches an infrared fixed point that is independent of the initial short distance dynamics that defines the material.
Observables, such as critical exponents usually depend only upon dimension of space, and are independent of the atomic or molecular constituents.
In the Standard Model, quarks and leptons have "Yukawa couplings" to the Higgs boson which determine the masses of the particles.
This equation describes how the Yukawa coupling changes with energy scale
The Yukawa couplings of the up, down, charm, strange and bottom quarks, are small at the extremely high energy scale of grand unification,
is increased slightly at the low energy scales at which the quark masses are generated by the Higgs,
On the other hand, solutions to this equation for large initial values typical for the top quark
cause the expression on the right side to quickly approach zero as we descend in energy scale, which stops
This is known as a (infrared) quasi-fixed point of the renormalization group equation for the Yukawa coupling.
The renormalization group equation for large values of the top Yukawa coupling was first considered in 1981 by Pendleton & Ross,[4] and the "infrared quasi-fixed point" was proposed by Hill.
[5] The prevailing view at the time was that the top quark mass would lie in a range of 15 to 26 GeV.
The quasi-infrared fixed point emerged in top quark condensation theories of electroweak symmetry breaking in which the Higgs boson is composite at extremely short distance scales, composed of a pair of top and anti-top quarks.
Since the observed top quark mass of 174 GeV is slightly lower than the standard model prediction by about 20%, this suggests there may be more Higgs doublets beyond the single standard model Higgs boson.
If there are many additional Higgs doublets in nature the predicted value of the quasi-fixed point comes into agreement with experiment.
[7][8] Even if there are two Higgs doublets, the fixed point for the top mass is reduced, 170~200 GeV.
Some theorists believed this was supporting evidence for the Supersymmetric Standard Model, however no other signs of supersymmetry have emerged at the Large Hadron Collider.