Top quark

Top Quark

Composition	Elementary particle
Family	QuarkFermion
Generation	Third
Symbol	t
Discovered	CDF and D0 collaborations, 1995
Mass	174.2±3.3 GeV/c2
Decays into	W boson and bottom quark
Electric charge	+2/3 e
Spin	½

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 currently measured at 174.2±3.3GeV, nearly as heavy as a gold nucleus.

The top quark interacts primarily by the strong interaction but can only decay via the weak force. It almost exclusively decays to a W boson and a bottom quark. The Standard Model predicts its lifetime to be roughly 1×10⁻²⁵ seconds; this is about 20 times faster 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 electroweak 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 this precision calculation 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 top and bottom instead.

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 2008).

Production and decay

As of 2007, 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 D0 Collaboration at Fermilab.

Mass and electroweak symmetry breaking

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.

${\mathcal {L}}=y_{t}hqu^{c}\rightarrow {\frac {y_{t}v}{\sqrt {2}}}(1+h^{0}/v)uu^{c}$

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

The top quark's large Yukawa coupling is indirect evidence for an elementary Higgs boson (in contrast to a composite Higgs boson).

Yukawa coupling

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 properties change depending on how they are probed. 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 its renormalization group flow rather than its high energy value. If a quark Yukawa couplings starts off at a small value then its value exponentially grows at low energy. If a Yukawa coupling starts off at a large value, then its value drops quadratically. At some point these two effects cancel and its value will not grow or shrink. This value is known as a fixed point of the renormalization group equation. If the renormalization group is followed long enough, no matter what the initial starting value of the coupling was, it will reach this fixed point.

The top quark Yukawa coupling lies near the fixed point of its Standard Model renormalization group equation

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

where $g_{3}$ is the color gauge coupling and $g_{2}$ is the weak isospin gauge coupling. The Yukawa coupling by itself drives the coupling lower, but the color gauge coupling drives it higher. The approximate value of the fixed point leads to a top quark mass of 280 GeV.

In the minimal supersymmetric extension of the Standard Model (the MSSM), the renormalization group equation for the top quark Yukawa coupling is modified to be

$\mu {\frac {\partial }{\partial \mu }}y_{t}\approx {\frac {y_{t}}{16\pi ^{2}}}\left(6y_{t}^{2}+y_{b}^{2}-{\frac {16}{3}}g_{3}^{2}-3g_{2}^{2}-{\frac {13}{15}}g_{1}^{2}\right)$,

where $y_{b}$ is the bottom quark Yukawa coupling. This leads to a fixed point where the top mass is 170–200 GeV. The uncertainty in this prediction is because the bottom quark Yukawa coupling can be amplified in the MSSM if we make $\tan \beta$ large enough. Some theorists believe that the MSSM fixed-point top quark mass being closer to the observed value of the top mass than the SM prediction is tentative evidence for the MSSM.

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 m_t = 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 170.9±1.8 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.

External links

• Tevatron Electroweak Working Group
• Top quark information on Fermilab website
• Logbook pages from CDF and DZero collaborations' top quark discovery
• Public Homepage of Top Quark Analysis Results from D0 Collaboration at Fermilab
• Public Homepage of Top Quark Analysis Results from CDF Collaboration at Fermilab
• Harvard Magazine article about the 1994 top quark discovery
• Top Quark Production and Properties at the Tevatron (June 2005)
• 1999 Nobel Prize in Physics