Top quark

The top quark, sometimes also referred to as the truth quark, (symbol: t) is the most massive of all observed

${\displaystyle y_{t}}$

Like all other

The top quark interacts with

Because the top quark is so massive, its properties allowed indirect determination of the mass of the Higgs boson (see § Mass and coupling to the Higgs boson below). As such, the top quark's properties are extensively studied as a means to discriminate between competing theories of new physics beyond the Standard Model. The top quark is the only quark that has been directly observed due to its decay time being shorter than the hadronization time.^[b][6]

History

In 1973,

• At the final Tevatron energy of 1.96 TeV, top–antitop pairs were produced with a
  pb
  .
• The W bosons from top quark decays carry polarization from the parent particle, hence pose themselves as a unique probe to top polarization.
• In the Standard Model, the top quark is predicted to have a spin quantum number of  1 /2 and electric charge ++ 2 /3. A first measurement of the top quark charge has been published, resulting in some confidence that the top quark charge is indeed ++ 2 /3.[21]

Production

Because top quarks are very massive, large amounts of energy are needed to create one. The only way to achieve such high energies is through high-energy collisions. These occur naturally in the Earth's upper atmosphere as

Top-quark pairs

gluon–gluon fusion

t-channel

quark–antiquark annihilation

The most common is

s-channel

t-channel

tW channel

The production of single top quarks via

Decay

The only known way the top quark can decay is through the weak interaction, producing a W boson and a bottom quark.^[a] Because of its enormous mass, the top quark is extremely short-lived, with a predicted lifetime of only 5×10⁻²⁵ s.^[5] As a result, top quarks do not have time before they decay to form hadrons as other quarks do.^[b] The absence of a hadron surrounding the top quark provides physicists with the unique opportunity to study the behavior of a "bare" quark.

In particular, it is possible to directly determine the

${\displaystyle \operatorname {B} \left(\ \mathrm {t} \to W^{+}\ \mathrm {b} \ \right)\equiv {\frac {\operatorname {\Gamma } \left(\ \mathrm {t} \to W^{+}\ \mathrm {b} \ \right)}{\ \sum _{q\ =\ \mathrm {b,s,d} }\operatorname {\Gamma } \left(\ \mathrm {t} \to W^{+}\ q\ \right)\ }}~.}$

The best current determination of this ratio is 0.957±0.034.^[25] Since this ratio is equal to |V_tb|² according to the Standard Model, this gives another way of determining the CKM element |V_tb|, or in combination with the determination of |V_tb| from single top production provides tests for the assumption that the CKM matrix is unitary.^[26]

The Standard Model also allows more exotic decays, but only at one loop level, meaning that they are extremely rare. In particular, it is conceivable that a top quark might decay into another up-type quark (an up or a charm) by emitting a photon or a Z-boson.

The Standard Model generates fermion masses through their couplings to the Higgs boson. This Higgs boson acts as a field filling space. Fermions interact with this field in proportion to their individual coupling constants ${\displaystyle \ y_{i}\ ,}$ which generates mass. A low-mass particle, such as the electron has a minuscule coupling ${\displaystyle \ y_{\text{electron}}=2\times 10^{-6}\ ,}$ while the top quark has the largest coupling to the Higgs, ${\displaystyle \ y_{\text{t}}\simeq 1~.}$

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, 10¹⁵ 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 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,^[28] and by Christopher T. Hill,^[29] 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:

${\displaystyle \mu \ {\frac {\ \partial }{\partial \mu }}\ y_{\mathrm {t} }\approx {\frac {\ y_{\text{t}}\ }{16\ \pi ^{2}}}\left({\frac {\ 9\ }{2}}y_{\mathrm {t} }^{2}-8g_{3}^{2}-{\frac {\ 9\ }{4}}g_{2}^{2}-{\frac {\ 17\ }{20}}g_{1}^{2}\right)\ ,}$

where g₃ is the color gauge coupling, g₂ is the weak isospin gauge coupling, and g₁ is the weak hypercharge gauge coupling. This equation describes how the Yukawa coupling changes with energy scale μ. Solutions to this equation for large initial values y_t cause the right-hand side of the equation to quickly approach zero, locking y_t to the QCD coupling g₃.

The value of the top quark fixed point is fairly precisely determined in the Standard Model, leading to a top-quark mass of 220 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

• CDF experiment
• Quark model
• Top quark condensate
• Topcolor
• Topness

Footnotes

References