Editing Top quark (section)

== Mass and coupling to the Higgs boson ==
The Standard Model generates fermion masses through their couplings to the [[Higgs boson]].  This Higgs boson acts as a field that fills space. Fermions interact with this field in proportion to their individual coupling constants {{math|''y''{{sub|''i''}}}}, which generates mass. A low-mass particle, such as the [[electron]] has a minuscule coupling {{nowrap|1={{math|''y''}}{{sub|electron}} = {{val|2|e=-6}}}}, while the top quark has the largest coupling to the Higgs, {{nowrap|{{math|''y''}}{{sub|t}} ≈ 1}}.

In the Standard Model, all of the quark and lepton Higgs–Yukawa couplings are small compared to the top-quark Yukawa coupling. This hierarchy in the fermion masses remains a profound and open problem in theoretical physics. Higgs–Yukawa couplings are not fixed constants of nature, as their values vary slowly as the energy scale (distance scale) at which they are measured. These dynamics of Higgs–Yukawa couplings, called "running coupling constants", are due to a quantum effect called the [[renormalization group]].

The Higgs–Yukawa couplings of the up, down, charm, strange and bottom quarks are hypothesized to have small values at the extremely high energy scale of grand unification, {{val|e=15|u=GeV}}. They increase in value at lower energy scales, at which the quark masses are generated by the Higgs. The slight growth is due to corrections from the [[Quantum chromodynamics|QCD]] coupling. The corrections from the Yukawa couplings are negligible for the lower-mass quarks.

One of the prevailing views in particle physics is that the size of the top-quark Higgs–Yukawa coupling is determined by a unique nonlinear property of the [[renormalization group]] equation that describes the ''running'' of the large Higgs–Yukawa coupling of the top quark. If a quark Higgs–Yukawa coupling has a large value at very high energies, its Yukawa corrections will evolve downward in mass scale and cancel against the QCD corrections. This is known as a (quasi-) [[infrared fixed point]], which was first predicted by B. Pendleton and G.G. Ross,<ref name=PendletonRoss/> and by [[Christopher T. Hill]],<ref name=Hill1981/> No matter what the initial starting value of the coupling is, if sufficiently large, it will reach this fixed-point value. The corresponding quark mass is then predicted.

The top-quark Yukawa coupling lies very near the [[infrared fixed point]] of the Standard Model. The renormalization group equation is:

<math display="block">\mu\ \frac{\ \partial}{\partial\mu}\ y_\mathrm{t} \approx \frac{\ y_\text{t}\ }{16\ \pi^2}\left(\frac{\ 9\ }{2}y_\mathrm{t}^2 - 8 g_3^2- \frac{\ 9\ }{4}g_2^2 - \frac{\ 17\ }{20} g_1^2 \right)\ ,</math>

where {{mvar|g}}{{sub|3}} is the color gauge coupling, {{mvar|g}}{{sub|2}} is the weak isospin gauge coupling, and {{mvar|g}}{{sub|1}} is the weak hypercharge gauge coupling. This equation describes how the Yukawa coupling changes with energy scale&nbsp;{{mvar|μ}}. Solutions to this equation for large initial values {{mvar|y}}{{sub|t}} cause the right-hand side of the equation to quickly approach zero, locking {{mvar|y}}{{sub|t}} to the QCD coupling {{mvar|g}}{{sub|3}}.

The value of the top quark fixed point is fairly precisely determined in the Standard Model, leading to a top-quark mass of 220&nbsp;GeV. This is about 25% larger than the observed top mass and may be hinting at new physics at higher energy scales.

The quasi-infrared fixed point subsequently became the basis of [[top quark condensation]] and [[topcolor]] theories of electroweak symmetry breaking, in which the Higgs boson is composed of a pair of top and antitop quarks. The predicted top-quark mass comes into improved agreement with the fixed point if there are additional Higgs scalars beyond the standard model and therefore it may be hinting at a rich spectroscopy of new Higgs fields at energy scales that can be probed with the LHC and its upgrades.<ref name=Hill2019a/><ref name=Hill2019b/>