Definitions

# Top quark

The top quark is the third-generation up-type quark with a charge of +(2/3)e. It was discovered in 1995 by the CDF and D0 experiments at Fermilab, and is by far the most massive of known elementary particles. Its mass is measured at , about the same weight as the nuclei of tantalum or tungsten atoms.

The top quark interacts primarily by the strong interaction but can only decay through the weak force. It almost exclusively decays to a W boson and a bottom quark. The Standard Model predicts its lifetime to be roughly ; this is about 20 times shorter than the timescale for strong interactions, and therefore it does not hadronize, giving physicists a unique opportunity to study a "bare" quark.

## History

In the years leading up to the top quark discovery, it was realized that certain precision measurements of the electro-weak vector boson masses and couplings are very sensitive to the value of the top quark mass. These effects become much larger for higher values of the top mass and therefore could indirectly see the top quark even if it could not be directly produced in any experiment at the time. The largest effect from the top quark mass was on the T parameter and by 1994 the precision of these indirect measurements had led to a prediction of the top quark mass to be between 145 GeV and 185 GeV. It is the development of techniques that ultimately allowed such precision calculations that led to Gerardus 't Hooft and Martinus Veltman winning the Nobel Prize in physics in 1999.

After the discovery of the first third-generation quark, an attempt was made to name it "beauty" and the predicted sixth quark "truth"; however, this later gave way to the names bottom and top.

The top quark was discovered in 1995 at Fermilab, whose Tevatron accelerator remains the only particle accelerator energetic enough to produce top quarks (until the LHC at CERN comes on-line in 2009).

## Production and decay

As of 2008, Fermilab's Tevatron is the only place in the world where top quarks can be produced. Tevatron is an accelerator complex which collides protons and antiprotons at center-of-momentum energy of 1.96 TeV. There are two main top-production processes:

• Pair production via strong interactions. This process was first observed simultaneously by two experimental collaboration at Fermilab, CDF and D0 in 1995.
• Single production via weak interactions. As of December 2006, a three-sigma evidence has been observed for this production process by the D0 Collaboration at Fermilab.

The top quark is expected to decay to a W boson and a down-type quark (down, strange or bottom). In the standard model, the branching fraction for t→Wq is predicted to be |Vtq|2, where Vtq is an element in the CKM matrix. The predictions for the branching ratios of the top quark are then B(t→Wd)≈0.006%, B(t→Ws)≈0.17% and B(t→Wb)≈99.8%.

## Top quark mass and relationship to the Higgs boson

The Standard Model describes fermion masses through the Higgs mechanism. The Higgs boson has a Yukawa coupling to the left- and right-handed top quarks. After electroweak symmetry breaking (when the Higgs acquires a vacuum expectation value), the left- and right-handed components mix, becoming a mass term.

$mathcal\left\{L\right\} = y_t h q u^c rightarrow frac\left\{y_t v\right\}\left\{sqrt\left\{2\right\}\right\}\left(1 + h^0/v\right) u u^c$

The top quark Yukawa coupling has a value of $y_t = sqrt\left\{2\right\} m_t/v simeq 1$, where $v=246~\left\{rm GeV\right\}$ is the value of the Higgs vacuum expectation value.

### Yukawa couplings

In the Standard Model, all of the quark and lepton Yukawa couplings are small compared to the top quark Yukawa coupling. Understanding this hierarchy in the fermion masses is an open problem in theoretical physics. Yukawa couplings are not constants and their values change depending on what energy scale (distance scale) at which they are measured. The dynamics of Yukawa couplings are determined by the renormalization group equation.

One of the prevailing views in particle physics is that the size of the top quark Yukawa coupling is determined by the renormalization group, leading to the "quasi-infrared fixed point."

The 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.

If, however, a quark Yukawa coupling has a large value at very high energies, its Yukawa corrections will evolve and cancel against the QCD corrections. This is known as a (quasi-) infrared fixed point. No matter what the initial starting value of the coupling is, if it is 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:

$mu frac\left\{partial\right\}\left\{partialmu\right\} y_t approx frac\left\{y_t\right\}\left\{16pi^2\right\}left\left(frac\left\{9\right\}\left\{2\right\}y_t^2 - 8 g_3^2- frac\left\{9\right\}\left\{4\right\}g_2^2 - frac\left\{17\right\}\left\{20\right\} g_1^2 right\right)$,

where $g_3$ is the color gauge coupling and $g_2$ is the weak isospin gauge coupling. This equation describes how the Yukawa coupling changes with energy scale $mu$. 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 $g_3$. The value of the fixed point is fairly precisely determined in the Standard Model, leading to a top quark mass of 230  GeV. However, if there is more than one Higgs doublet, the mass value will be reduced by Higgs mixing angle effects in an unpredicted way.

In the minimal supersymmetric extension of the Standard Model (the MSSM), there are two Higgs doublets and the renormalization group equation for the top quark Yukawa coupling is slightly modified:

$mu frac\left\{partial\right\}\left\{partialmu\right\} y_t approx frac\left\{y_t\right\}\left\{16pi^2\right\}left\left(6y_t^2 +y_b^2- frac\left\{16\right\}\left\{3\right\} g_3^2- 3g_2^2 -frac\left\{13\right\}\left\{15\right\} g_1^2 right\right)$,

where $y_b$ is the bottom quark Yukawa coupling. This leads to a fixed point where the top mass is smaller, 170–200 GeV. The uncertainty in this prediction arises because the bottom quark Yukawa coupling can be amplified in the MSSM. Some theorists believe this is supporting evidence for the MSSM.

The quasi-infrared fixed point has subsequently formed the basis of 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.

## Properties

• At the current Tevatron energy of 1.96 TeV, top/anti-top pairs are produced with a cross section of about 7 picobarns. The Standard Model prediction (at next-to-leading order with mt = 175 GeV) is 6.7–7.5 picobarns.
• Combining measurements from both CDF and D0, the most recent estimation of the top quark mass is 172.6±1.4 GeV/c2.
• Production of single top quarks through weak vector bosons is predicted in the Standard Model and has a cross section of 0.9 picobarns in the s-channel and 2.0 picobarns in the t-channel. Neither experiment at the Tevatron has observed this process with statistical significance. However, on 8 December 2006, the D0 collaboration announced it had seen evidence for single top production at the 3 sigma level, measuring an s+t channel cross section of 4.9 picobarns. A preprint article submitted to Physical Review Letters is available from the arXiv.org preprint server.
• 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, top quark is predicted to have a spin of ½ and charge ⅔. A first measurement of the top quark charge has been published, resulting in approximately 90% confidence limit that the top quark charge is indeed ⅔.