Indicator function: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
en>UKoch
wording, math formulae, boldface only for 1st occurrence of lemma, list format
en>Qwertyus
Added {{merge from}} tag to article (TW)
Line 1: Line 1:
{{Infobox Particle
Title of the author is definitely Gabrielle Lattimer. For years she's been working even though a library assistant. For a while she's yet been in Massachusetts. As a woman what your sweetheart really likes is mah jongg but she doesn't have made a dime utilizing it. She could be described as running and maintaining the best blog here: http://prometeu.net<br><br>Review my web blog - [http://prometeu.net clash of clans cheat]
|bgcolour    =
|name        = Top quark
|image      = [[Image:Top antitop quark event.svg|200px]]
|caption    = A collision event involving top quarks
|num_types  =
|composition = [[Elementary particle]]
|statistics  = [[Fermionic]]
|group      = [[Quark]]
|generation  = Third
|interaction = [[Strong interaction|Strong]], [[Weak interaction|Weak]], [[Electromagnetic force]], [[Gravity]]
|particle    =
|antiparticle= Top antiquark ({{SubatomicParticle|Top antiquark}})
|theorized  = [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]] (1973)
|discovered  = [[Collider Detector at Fermilab|CDF]] and [[D0 experiment|DØ]] collaborations (1995)
|symbol      = {{SubatomicParticle|Top quark}}
|mass        = 173.07 ± 0.52 (stat) ± 0.72 (syst){{val|ul=GeV/c2}}<ref name="PDG2013">
{{cite web
|author=J. Beringer ''et al.'' ([[Particle Data Group]])
|url=http://pdg.lbl.gov/2013/tables/rpp2013-sum-quarks.pdf
|title=PDGLive Particle Summary 'Quarks (u, d, s, c, b, t, b', t', Free)'
|publisher=[[Particle Data Group]]
|year=2012
|accessdate=2013-07-23
}}</ref>
|decay_time      = {{val|5|e=-25|u=s}}
|decay_particle  = {{nowrap|[[bottom quark]] (99.8%)}}<br/>{{nowrap|[[strange quark]] (0.17%)}}<br>{{nowrap|[[down quark]] (0.007%)}}
|electric_charge = +{{frac|2|3}} [[Elementary charge|e]]
|color_charge    = Yes
|spin            = {{frac|1|2}}
|topness        = 1
|weak_isospin    = {{frac|1|2}} (left handed)<br/> 0 (right handed)
|weak_hypercharge= {{frac|1|3}} (left handed)<br/> {{frac|4|3}} (right handed)
}}
 
The '''top quark''', also known as the '''t quark''' (symbol: t) or '''truth quark''', is an [[elementary particle]] and a fundamental constituent of [[matter]]. Like all [[quark]]s, the top quark is an [[elementary particle|elementary]] [[fermion]] with [[spin (physics)|spin]]-[[spin-½|{{frac|1|2}}]], and experiences all four [[fundamental interaction]]s: [[gravitation]], [[electromagnetism]], [[weak interaction]]s, and [[strong interaction]]s. It has an [[electric charge]] of +{{frac|2|3}}&nbsp;[[elementary charge|e]],<ref name="Willenbrock">{{cite book
|author=S. Willenbrock
|year=2003
|chapter=The Standard Model and the Top Quark
|editor=H.B Prosper and B. Danilov (eds.)
|title=Techniques and Concepts of High-Energy Physics XII
|url=http://books.google.com/?id=HXm6M_YUzoYC&pg=PA1&lpg=PA1&dq=quark+%22standard+model%22
|series=NATO Science Series
|volume=123 |pages=1–41
|publisher=[[Kluwer Academic]]
|isbn=1-4020-1590-9
|arxiv=hep-ph/0211067v3
}}</ref> and is the most massive of all observed [[elementary particle]]s. It has a [[Quark#Mass|mass]] of 173.07 ± 0.52 (stat) ± 0.72 (syst){{val|ul=GeV/c2}},<ref name="PDG2013"/> which is about the same mass as an [[atom]] of [[tungsten]].<!--172.9 GeV/c^2 * 0.931494061 GeV/c^2/u = 185.2937203 atomic mass units. The most common isotope of tungsten is 184W, which has a mass of 183.950928u. The most common isotope of rhenium is 187Re, which has a mass of 186.955744u. Thus tungsten is the heaviest element that is lighter than the top quark.--> The [[antiparticle]] of the top quark is the '''top antiquark''' (symbol: {{overline|t}}, sometimes called ''antitop quark'' or simply ''antitop''), which differs from it only in that some of its properties have [[additive inverse|equal magnitude but opposite sign]].
 
The top quark interacts primarily by the [[strong interaction]] but can only decay through the [[weak force]]. It decays almost exclusively to a [[W boson]] and a [[bottom quark]], but it can decay also into a [[strange quark]], and on the rarest of occasions, into a [[down quark]]. The [[Standard Model]] predicts its [[mean lifetime]] to be roughly {{val|5|e=-25|u=s}}.<ref name=Quadt>
{{cite journal
|author=A. Quadt
|year=2006
|title=Top quark physics at hadron colliders
|journal=[[European Physical Journal C]]
|volume=48
|issue=3 |pages=835–1000
|doi=10.1140/epjc/s2006-02631-6
|bibcode = 2006EPJC...48..835Q }}</ref> This is about 20&nbsp;times shorter than the timescale for strong interactions, and therefore it does not [[Hadronization|form hadrons]], giving physicists a unique opportunity to study a "bare" quark (all other quarks [[Hadronization|hadronize]], meaning they combine with other quarks to form [[hadron]]s, and can only be observed as such). Because it is so massive, the properties of the top quark allow predictions to be made of the mass of the [[Higgs boson]] under certain [[Beyond the Standard Model|extensions of the Standard Model]] (see [[#Mass and coupling to the Higgs boson|Mass and coupling to the Higgs boson]] below). As such, it is extensively studied as a means to discriminate between competing theories.
 
Its existence (and that of the [[bottom quark]]) was postulated in 1973 by [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]] to explain the observed [[CP violation]]s in [[kaon]] [[particle decay|decay]],<ref name="M. Kobayashi, T. Maskawa 1973 652">
{{cite journal
|author=M. Kobayashi, T. Maskawa
|year=1973
|title=''CP''-Violation in the Renormalizable Theory of Weak Interaction
|journal=[[Progress of Theoretical Physics]]
|volume=49
|issue=2 |page=652
|doi=10.1143/PTP.49.652
|bibcode = 1973PThPh..49..652K }}</ref> and was discovered in 1995 by the [[Collider Detector at Fermilab|CDF]]<ref name=CDF-1995>
{{cite journal
|author=F. Abe ''et al''. ([[CDF Collaboration]])
|year=1995
|title=Observation of Top Quark Production in {{SubatomicParticle|Antiproton}}{{SubatomicParticle|Proton}} Collisions with the Collider Detector at Fermilab
|journal=[[Physical Review Letters]]
|volume=74
|issue=14 |pages=2626–2631
|doi=10.1103/PhysRevLett.74.2626
|pmid=10057978
|bibcode=1995PhRvL..74.2626A
}}</ref> and [[DØ experiment|DØ]]<ref name=D0-1995>
{{cite journal
|author=S. Abachi ''et al''. ([[DØ Collaboration]])
|year=1995
|title=Search for High Mass Top Quark Production in {{SubatomicParticle|Proton}}{{SubatomicParticle|Antiproton}} Collisions at {{radical|''s''}}&nbsp;=&nbsp;1.8&nbsp;TeV
|journal=[[Physical Review Letters]]
|volume=74
|issue=13 |pages=2422–2426
|doi=10.1103/PhysRevLett.74.2422
|bibcode=1995PhRvL..74.2422A
}}</ref> experiments at [[Fermilab]]. Kobayashi and Maskawa won the [[List of Nobel laureates in Physics|2008 Nobel Prize in Physics]] for the prediction of the top and [[bottom quark]], which together form the third [[Generation (particle physics)|generation]] of quarks.<ref>
{{cite web
|year=2008
|title=2008 Nobel Prize in Physics
|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html
|publisher=[[The Nobel Foundation]]
|accessdate=2009-09-11
}}</ref>
 
==History==
In 1973, [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]] predicted the existence of a third generation of quarks to explain observed [[CP violation]]s in [[kaon]] [[particle decay|decay]].<ref name="M. Kobayashi, T. Maskawa 1973 652"/> The names top and [[bottom quark|bottom]] were introduced by [[Haim Harari]] in 1975,<ref>
{{cite journal
|author=H. Harari
|year=1975
|title=A new quark model for hadrons
|journal=[[Physics Letters B]]
|volume=57 |issue=3 |page=265
|doi=10.1016/0370-2693(75)90072-6
|bibcode = 1975PhLB...57..265H }}</ref><ref>
{{cite book
|author=K.W. Staley
|year=2004
|title=The Evidence for the Top Quark
|url=http://books.google.com/?id=K7z2oUBzB_wC
|pages=31–33
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-82710-2
}}</ref>
to match the names of the first generation of quarks ([[up quark|up]] and [[down quark|down]]) reflecting the fact that the two were the 'up' and 'down' component of a [[weak isospin]] [[Doublet (physics)|doublet]].<ref name="DHPerkins">
{{cite book
|author=D.H. Perkins
|title=Introduction to high energy physics
|page=8
|publisher=[[Cambridge University Press]]
|year=2000
|isbn=0-521-62196-8
}}</ref> The top quark was sometimes called ''truth quark'' in the past, but over time ''top quark'' became the predominant use.<ref name=Close2006>
{{cite book
|author=F. Close
|title=The New Cosmic Onion
|page=133
|publisher=[[CRC Press]]
|year=2006
|isbn=1-58488-798-2
}}</ref>
 
The proposal of Kobayashi and Maskawa heavily relied on the [[GIM mechanism]] put forward by [[Sheldon Lee Glashow]], [[John Iliopoulos]] and [[Luciano Maiani]],<ref>
{{cite journal
|author=S.L. Glashow, J. Iliopoulous, L. Maiani
|year=1970
|title=Weak Interactions with Lepton–Hadron Symmetry
|journal=[[Physical Review D]]
|volume=2
|issue=7 |pages=1285–1292
|doi=10.1103/PhysRevD.2.1285
|bibcode = 1970PhRvD...2.1285G }}</ref> which predicted existence of the then still unobserved [[charm quark]]. When in [[November Revolution (physics)|November 1974]] teams at [[Brookhaven National Laboratory]] (BNL) and the [[Stanford Linear Accelerator Center]] (SLAC) simultaneously announced the discovery of the [[J/ψ meson]], it was soon after identified as a bound state of the missing charm quark with its antiquark. This discovery allowed the GIM mechanism to become part of the Standard Model.<ref>
{{cite book
|author=A. Pickering
|year=1999
|title=Constructing Quarks: A Sociological History of Particle Physics
|pages=253–254
|publisher=[[University of Chicago Press]]
|isbn=978-0-226-66799-7
}}</ref> With the acceptance of the GIM mechanism, Kobayashi and Maskawa's prediction also gained in credibility. Their case was further strengthened by the discovery of the [[tau (particle)|tau]] by [[Martin Lewis Perl]]'s team at SLAC between 1974 and 1978.<ref name="Perl1975">
{{cite journal
|author=M.L. Perl ''et al.''
|year=1975
|title=Evidence for Anomalous Lepton Production in {{SubatomicParticle|Positron}}{{SubatomicParticle|Electron}} Annihilation
|journal=[[Physical Review Letters]]
|volume=35 |issue=22 |page=1489
|doi=10.1103/PhysRevLett.35.1489
|bibcode=1975PhRvL..35.1489P
}}</ref> This announced a third generation of [[leptons]], breaking the new [[symmetry (physics)|symmetry]] between leptons and quarks introduced by the GIM mechanism. Restoration of the symmetry implied the existence of a fifth and sixth quark.
 
It was in fact not long until a fifth quark, the bottom, was discovered by the [[E288 experiment]] team, led by [[Leon Lederman]] at [[Fermilab]] in 1977.<ref>
{{cite press
|date=7 August 1977
|title=Discoveries at Fermilab – Discovery of the Bottom Quark
|url=http://www.fnal.gov/pub/inquiring/physics/discoveries/bottom_quark_pr.html
|publisher=[[Fermilab]]
|accessdate=2009-07-24
}}</ref><ref>
{{cite journal
|author=L.M. Lederman
|year=2005
|url=http://www.symmetrymagazine.org/cms/?pid=1000195
|title=Logbook: Bottom Quark
|journal=[[Symmetry Magazine]]
|volume=2 |issue=8 |pages=
}}</ref><ref>
{{cite journal
|author=S.W. Herb ''et al''.
|year=1977
|title=Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions
|journal=[[Physical Review Letters]]
|volume=39
|issue=5 |page=252
|doi=10.1103/PhysRevLett.39.252
|bibcode=1977PhRvL..39..252H
}}</ref> This strongly suggested that there must also be a sixth quark, the top, to complete the pair. 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.<ref name=LissTipton1997>
{{cite journal
|author=T.M. Liss, P.L. Tipton
|year=1997
|title=The Discovery of the Top Quark
|url=http://www.hep.uiuc.edu/home/tml/SciAmTop.pdf
|journal=[[Scientific American]]
|volume= |issue= |pages=54–59
}}</ref>
 
Early searches for the top quark at [[SLAC]] and [[DESY]] (in [[Hamburg]]) came up empty-handed. When in the early eighties the [[Super Proton Synchrotron]] (SPS) at [[CERN]] discovered the [[W&nbsp;boson]] and the [[Z&nbsp;boson]], it was again felt that the discovery of the top was imminent. As the SPS gained competition 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 {{val|41|u=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 {{val|77|u=GeV/c2}}.<ref name=LissTipton1997/>
 
The Tevatron was (until the start of [[Large Hadron Collider|LHC]] operation at [[CERN]] in 2009) the only hadron collider powerful enough to produce top quarks. In order to be able to confirm a future discovery, a second detector, the [[DZero experiment|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&nbsp;22, 1994, the CDF group submitted their paper presenting tentative evidence for the existence of a top quark with a mass of about {{val|175|u=GeV/c2}}. In the meantime DØ had found no more evidence than the suggestive event in 1992. A year later on March&nbsp;2, 1995, 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 {{val|176|18|u=GeV/c2}}.<ref name=CDF-1995/><ref name=D0-1995/><ref name=LissTipton1997/>
 
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 [[S and T parameters|T&nbsp;parameter]] and by 1994 the precision of these indirect measurements had led to a prediction of the top quark mass to be between {{val|145|u=GeV/c2}} and {{val|185|u=GeV/c2}}.{{Citation needed|date=July 2009}} 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.<ref>
{{cite web
|publisher=[[The Nobel Foundation]]
|title=The Nobel Prize in Physics 1999
|url=http://nobelprize.org/nobel_prizes/physics/laureates/1999/index.html
|accessdate=2009-09-10
}}</ref><ref>
{{cite press
|publisher=[[The Nobel Foundation]]
|date=12 October 1999
|title=The Nobel Prize in Physics 1999, Press Release
|url=http://nobelprize.org/nobel_prizes/physics/laureates/1999/press.html
|accessdate=2009-09-10
}}</ref>
 
==Properties==
* At the final Tevatron energy of 1.96&nbsp;TeV, top–antitop pairs were produced with a [[Cross section (physics)|cross section]] of about 7&nbsp;[[picobarn]]s (pb).<ref>
{{cite conference
|author=D. Chakraborty ([[DØ collaboration|DØ]] and [[CDF collaboration]]s)
|year=2002
|title=Top quark and W/Z results from the Tevatron
|conference=[[Rencontres de Moriond]]
|url=http://www-d0.fnal.gov/d0pubs/sbdata/2002/020316-CHAKRABORTY_D-talk.pdf
|page=26
}}</ref> The [[Standard Model]] prediction (at [[leading-order#Next-to-leading order|next-to-leading order]] with {{math|size=120%|''m''<sub>t</sub> {{=}} }}{{val|175|u=GeV/c2}}) is 6.7–7.5&nbsp;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 {{frac|1|2}} and electric charge +{{frac|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 +{{frac|2|3}}.<ref>
{{cite journal
|author=V.M. Abazov ''et al.'' ([[DØ Collaboration]])
|year=2007
|title=Experimental discrimination between charge 2''e''/3 top quark and charge 4''e''/3 exotic quark production scenarios
|journal=[[Physical Review Letters]]
|volume=98 |page=041801
|doi=10.1103/PhysRevLett.98.041801
|arxiv=hep-ex/0608044
|pmid=17358756
|issue=4
|bibcode=2007PhRvL..98d1801A
}}</ref>
 
==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 [[cosmic ray]]s collide with particles in the air, or can be created in a [[particle accelerator]]. As of 2011, the only operational accelerator that generates a beam of sufficient energy to produce top quarks is the [[Large Hadron Collider]] at [[CERN]], with a [[center-of-mass frame|center-of-mass energy]] of 7&nbsp;TeV.
 
There are multiple processes that can lead to the production of a top quark. The most common is [[pair production|production of a top–antitop pair]] via [[strong interaction]]s. In a collision a highly energetic [[gluon]] is created which subsequently decays into a top and antitop. This process was responsible for the majority of the top events at Tevatron and was the process observed when the top was first discovered in 1995.<ref name=D0-2009/> 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 virtually 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 an up or down quark ("t-channel"). The first evidence for these processes was published by the DØ collaboration in December 2006,<ref name=D0-2006>
{{cite journal
|author=V.M. Abazov ''et al.'' ([[DØ Collaboration]])
|year=2007
|title=Evidence for production of single top quarks and first direct measurement of {{!|}}V<sub>tb</sub>{{!}}
|journal=[[Physical Review Letters]]
|volume=98
|issue=18 |pages=181802
|doi=10.1103/PhysRevLett.98.181802
|arxiv=hep-ex/0612052
|bibcode=2007PhRvL..98r1802A
}}</ref> and in March 2009 the CDF<ref name=CDF-2009>
{{cite journal
|author=T. Aaltonen ''et al.'' ([[CDF Collaboration]])
|year=2009
|issue=9
|title=First Observation of Electroweak Single Top Quark Production
|volume=103
|doi=10.1103/PhysRevLett.103.092002
|journal=[[Physical Review Letters]]
|arxiv=0903.0885
|bibcode=2009PhRvL.103i2002A
}}</ref> and DØ<ref name=D0-2009>
{{cite journal
|author=V.M. Abazov ''et al.'' ([[DØ Collaboration]])
|year=2009
|issue=9
|title=Observation of Single Top Quark Production
|volume=103
|doi=10.1103/PhysRevLett.103.092001
|journal=Physical Review Letters
|arxiv=0903.0850
|bibcode=2009PhRvL.103i2001A
}}</ref> 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 {{math|size=120%|{{!}} ''V''<sub>tb</sub> {{!}}<sup>2</sup>}}&nbsp;component of the [[CKM matrix]].
 
==Decay==
The only known 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 {{val |5|e=-25|u=s}}.<ref name=Quadt /> As a result top quarks do not have time to [[hadronization|form hadrons]] before they decay, as other quarks do. This provides physicists with the unique opportunity to study the behavior of a "bare" quark.
 
In particular, it is possible to directly determine the [[branching ratio]] Γ(W<sup>+</sup>b)&nbsp;/&nbsp;Γ(W<sup>+</sup>''q''&nbsp;(''q''&nbsp;=&nbsp;b,s,d)). The best current determination of this ratio is {{val|0.91|0.04}}.<ref name=PDG2013/> Since this ratio is equal to {{math|size=120%|{{!}} ''V''<sub>tb</sub> {{!}}<sup>2</sup>}} according to the [[Standard Model]], this gives another way of determining the CKM element&nbsp;{{math|size=120%|{{!}} ''V''<sub>tb</sub> {{!}}}}, or in combination with the determination of {{math|size=120%|{{!}} ''V''<sub>tb</sub> {{!}}}} from single top production provides tests for the assumption that the CKM matrix is unitary.<ref name=Abazov2008>
{{cite journal
|author=V.M. Abazov ''et al.'' ([[DØ Collaboration]])
|year=2008
|title=Simultaneous measurement of the ratio B(t→Wb)/B(t→Wq) and the top-quark pair production cross section with the DØ detector at {{sqrt|''s''}}&nbsp;=&nbsp;1.96&nbsp;TeV
|journal=[[Physical Review Letters]]
|volume=100
|issue=19 |pages=192003
|doi=10.1103/PhysRevLett.100.192003
|arxiv=0801.1326
|bibcode=2008PhRvL.100s2003A
}}</ref>
 
The Standard Model also allows more exotic decays, but only at one loop level, meaning that they are extremely suppressed. In particular, it is possible for a top quark to decay into another up-type quark (an up or a charm) by emitting a photon or a Z-boson.<ref>
{{cite journal
|author=S. Chekanov ([[ZEUS Collaboration]])
|year=2003
|title=Search for single-top production in ep collisions at HERA
|journal=[[Physics Letters B]]
|volume=559
|issue=3–4 |page=153
|doi=10.1016/S0370-2693(03)00333-2
|arxiv=hep-ex/0302010
|bibcode = 2003PhLB..559..153Z }}</ref> Searches for these exotic decay modes have 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 5.9 in 1,000 for photonic decay and less than 2.1 in 1,000 for Z-boson decay at 95% [[confidence level|confidence]].<ref name=PDG2013/>
 
==Mass and coupling to the Higgs boson==
{{Refimprove section|date=July 2009}}
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.
 
:<math>\mathcal{L} = y_\text{t} h q u^c \rightarrow \frac{y_\text{t} v}{\sqrt{2}}( 1 + h^0/v) u u^c</math>
 
The top quark Yukawa coupling has a value of
 
:<math>y_\text{t} = \sqrt{2} m_\text{t}/v \simeq 1</math>
 
where {{math|''v'' {{=}} }}246&nbsp;GeV is the value of the Higgs [[vacuum expectation value]].
 
===Yukawa couplings===
{{See also|Beta function (physics)}}
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, 10<sup>15</sup>&nbsp;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.
 
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:
 
:<math>\mu \frac{\partial}{\partial\mu} y_\text{t} \approx \frac{y_\text{t}}{16\pi^2}\left(\frac{9}{2}y_\text{t}^2 - 8 g_3^2- \frac{9}{4}g_2^2 - \frac{17}{20} g_1^2 \right),</math>
 
where {{math|size=120%|''g''<sub>3</sub>}} is the color gauge coupling, {{math|size=120%|''g''<sub>2</sub>}} is the weak isospin gauge coupling, and {{math|size=120%|''g''<sub>1</sub>}} 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 {{math|size=120%|''y''<sub>t</sub>}} cause the right-hand side of the equation to quickly approach zero, locking {{math|size=120%|''y''<sub>t</sub>}} to the QCD coupling {{math|size=120%|''g''<sub>3</sub>}}. The value of the fixed point is fairly precisely determined in the Standard Model, leading to a top quark mass of 230&nbsp;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 Standard Model|minimal supersymmetric extension of the Standard Model]] (MSSM), there are two Higgs doublets and the renormalization group equation for the top quark Yukawa coupling is slightly modified:
 
:<math>\mu \frac{\partial}{\partial\mu} y_\text{t} \approx \frac{y_\text{t}}{16\pi^2}\left(6y_\text{t}^2 +y_\text{b}^2- \frac{16}{3} g_3^2- 3g_2^2 -\frac{13}{15} g_1^2 \right),</math>
 
where ''y''<sub>b</sub> is the bottom quark Yukawa coupling. This leads to a fixed point where the top mass is smaller, 170–200&nbsp;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 antitop quarks.
 
==See also==
*[[CDF experiment]]
*[[Topness]]
*[[Top quark condensate]]
*[[Topcolor]]
*[[Quark model]]
 
== References ==
{{reflist|2}}
 
==Further reading==
*{{cite arxiv
|date=June 2005
|title=Top Quark Production and Properties at the Tevatron
|class=hep-ex
|eprint=hep-ex/0506005
|author1=Frank Fiedler
|author2=for the D0
|author3=CDF Collaborations
}}
*{{cite web
|author=R. Nave
|title=Quarks
|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/quark.html
|work=[[HyperPhysics]]
|publisher=[[Georgia State University]], Department of Physics and Astronomy
|year=
|accessdate=2008-06-29
}}
*{{cite book
|author=A. Pickering
|title=Constructing Quarks
|pages=114–125
|publisher=[[University of Chicago Press]]
|year=1984
|isbn=0-226-66799-5
}}
 
== External links ==
* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=2&index1=234702 Top quark on arxiv.org]
* [http://tevewwg.fnal.gov/top/ Tevatron Electroweak Working Group]
* [http://www.fnal.gov/pub/inquiring/physics/discoveries/top_quark.html Top quark information on Fermilab website]
* [http://www.symmetrymag.org/cms/?pid=1000085 Logbook pages from CDF and DZero collaborations' top quark discovery]
* [http://web.hep.uiuc.edu/home/tml/SciAmTop.pdf Scientific American article on the discovery of the top quark]
* [http://www-d0.fnal.gov/Run2Physics/top/top_public_web_pages/top_public.html Public Homepage of Top Quark Analysis Results from DØ Collaboration at Fermilab]
* [http://www-cdf.fnal.gov/physics/new/top/top.html Public Homepage of Top Quark Analysis Results from CDF Collaboration at Fermilab]
* [http://www.agwright.com/writing/articles/hm_quark.htm Harvard Magazine article about the 1994 top quark discovery]
* [http://nobelprize.org/physics/laureates/1999/ 1999 Nobel Prize in Physics]
 
{{Particles}}
 
{{DEFAULTSORT:Top Quark}}
[[Category:Quarks]]
[[Category:Standard Model]]

Revision as of 23:23, 10 February 2014

Title of the author is definitely Gabrielle Lattimer. For years she's been working even though a library assistant. For a while she's yet been in Massachusetts. As a woman what your sweetheart really likes is mah jongg but she doesn't have made a dime utilizing it. She could be described as running and maintaining the best blog here: http://prometeu.net

Review my web blog - clash of clans cheat

Retrieved from "https://en.formulasearchengine.com/index.php?title=Indicator_function&oldid=226838"