Top quark

Top quark

Composition	Elementary particle
Family	QuarkFermion
Generation	Third
Interactions	Strong, Weak, Electromagnetic force, Gravity
Symbol	t
Antiparticle	Top antiquark ( t )
Theorized	Makoto Kobayashi and Toshihide Maskawa (1973)
Discovered	CDF and DØ collaborations (1995)
Mass	173.1±1.3 GeV/c2
Decays into	Bottom quark (99.8%), strange quark (0.17%), down quark (0.007%)
Electric charge	+2⁄3 e
Color charge	Yes
Spin	1⁄2
Topness	1
Weak isospin	1⁄2 (left handed) 0 (right handed)
Weak hypercharge	1⁄3 (left handed) 4⁄3 (right handed)

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 DØ experiments at Fermilab, and is the most massive of known elementary particles. (The Higgs boson, which may be as massive, has not yet been experimentally observed.) Its mass is measured at 173.1±1.3 GeV/c², about the same mass as an atom of rhenium.

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 0.5×10⁻²⁵ s. 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 1973, Makoto Kobayashi and Toshihide Maskawa predicted the existence of a third generation of quarks to explain observed CP violations in kaon decay. The new hypothetical particles were labelled t and b for top and bottom respectively. These names mirrored the names of the first generation of quarks (up and down) reflecting the fact that the two were the 'spin up' and 'spin down' component of a weak isospin doublet.

Soon after their prediction experimental searches started to the two new particles in particle colliders. The discovery of the bottom by Leon Lederman's team at Fermilab in 1977, strengthened the belief that there should be a sixth quark, the top. It was known that this quark would be heavier than the bottom, requiring more energy to create in particle collisions, but the general expectation was that the sixth quark would soon be found. However, it took another 18 years before the existence of the top was confirmed.

Early searches for the top quark at the Stanford Linear Accelerator Center and DESY in Hamburg came up empty-handed. When in the early eighties the Super Proton Synchrotron (SPS) at CERN discovered the W boson and the Z boson, it was again felt that the discovery of the top was imminent. As the SPS gained compitition from the Tevatron at Fermilab there was still no sign of the missing particle, and it was announced by the group at CERN that the top mass must be at least 41 GeV/c². After a race between CERN and Fermilab to discover the top, the accelerator at CERN reached its limits without creating a single top pushing the lower bound on its mass up to 77 GeV/c².

For the foreseeable futute, Tevatron would be the only hadron collider powerful enough to potentially produce the top. In order to be able to confirm a future discovery a second detector, the DØ detector, was added to the complex (in addition to the Collider Detector at Fermilab (CDF) already present). In October 1992, the two groups found their first hint of the top, with a single creation event that appeared to contain the top. In the following years more evidence was collected and on April 22, 1994 the CDF group published a paper presenting tentative evidence for the existence of a top quark with a mass of about 175 GeV/c². In the meantime DØ had found no more evidence than the suggestive event in 1992. A year later after having gathered more evidence and a reanalysis of the DØ data (who had been searching for a much lighter top), the two groups jointly reported the discovery of the top with a certainty of 99.9998% at a mass of 176±18 GeV/c².

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/c² and 185 GeV/c². 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.

Properties

• At the current Tevatron energy of 1.96 TeV, top/anti-top pairs are produced with a cross section of about 7 picobarns (pb). The Standard Model prediction (at next-to-leading order with m_t = 175 GeV/c²) is 6.7–7.5 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, top quark is predicted to have a spin of 1⁄2 and charge +2⁄3. A first measurement of the top quark charge has been published, resulting in approximately 90% confidence limit that the top quark charge is indeed +2⁄3.

Production

Because top quarks are very massive, a lot of energy is 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 cosmic rays collide with particles in the air, or can be created in a particle accelerator. As of 2009, the only operational accelerator that generates enough energy to produce top quarks is the Tevatron at Fermilab, in which protons and antiprotons are collided at a center-of-mass energy of 1.96 TeV.

There are multiple processes that can lead to the production of a top quark. The most common is production of a top-antitop pair via strong interactions. In a collision a highly energetic gluon is created which subsequently decays into a top and antitop. This process is responsible for the majority of the top events at Tevatron and is the process observed when the top was first discovered in 1995. It is also possible to produce pairs of top-antitop through the decay of an intermediate photon or Z-boson. However, these processes are predicted to be much rarer and have a vitually identical experimental signature in a hadron collider like Tevatron.

A distinctly different process is the production of single tops via weak interaction. This can happen in two ways (called channels) either an intermediate W-boson decays into a top and antibottom quark (s-channel) or a bottom quark (probably created in a pair through the decay of a gluon) transforms to top quark by exchanging a W-boson with a up or down quark (t-channel). The first evidence for these processes was published by the DØ collaboration in December 2006, and in March 2009 the CDF and DØ collaborations released twin papers with the definitive observation of these processes. The main significance of measuring these production processes is that their frequency is directly proportional to the |V_tb|² component of the CKM matrix.

Decay

The only know way that a top quark can decay is through the weak interaction producing a W-boson and a down-type quark (down, strange, or bottom). Because of its enormous mass, the top quark is extremely short lived with a predicted lifetime of only 0.5×10⁻²⁵ s. As a result top quarks do not have time to form hadrons before they decay, as other quarks do. This provides physicists with the unique opportunity the study the behaviour of a bare quark.

In particular, it is possible to directly determine the ratio of top quarks into bottom quarks. The best current determination of this ratio is 0.99+0.09
−0.08. 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.

The Standard Model also allows more exotic decays, but only at one loop level, meaning that they extremely suppressed. In particular, it is possible for a top quark to decay into an other up-type quark (an up or a charm) by emitting a photon or a Z-boson. Searches for these exotic decay modes how provided no evidence for their existence in accordance with expectations from the standard model. The branching ratios for these decays have been determined to be less than 6 in 1000 for photonic decay and less than 4 in 100 for Z-boson decay at 95% confidence.

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.

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

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.

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:

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

where $g_{3}$ is the color gauge coupling and $g_{2}$ is the weak isospin gauge coupling. 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:

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

where $y_{b}$ is the bottom quark Yukawa coupling. This leads to a fixed point where the top mass is 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.

External links

• Top quark on arxiv.org
• Tevatron Electroweak Working Group
• Top quark information on Fermilab website
• Logbook pages from CDF and DZero collaborations' top quark discovery
• Scientific American article on the discovery of the top quark
• Public Homepage of Top Quark Analysis Results from DØ 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