Geometric series: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>יהודה שמחה ולדמן
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{Infobox Particle
My name's Wendi Nyholm but everybody calls me Wendi. I'm from United States. I'm studying at the university (1st year) and I play the Bass Guitar for 5 years. Usually I choose music from the famous films ;). <br>I have two sister. I love Equestrianism, watching TV (Breaking Bad) and Skydiving.<br><br>Here is my blog ... [http://www.Centralparkaustin.com/2012/09/06/hello-world-2-2/ Fifa Coin Generator]
| bgcolour        =
| name           = Gluon
| image          = [[File:Feynmann Diagram Gluon Radiation.svg|200px]]
| caption        = In [[Feynman diagram]]s, emitted gluons are represented as spirals. This diagram depicts the [[Electron–positron_annihilation|annihilation of an electron and positron]].
| num_types      = 8
| composition    = [[Elementary particle]]
| statistics      = [[Bosonic]]
| group          = [[Gauge boson]]
| generation      =
| interaction    = [[Strong interaction]]
| theorized      = [[Murray Gell-Mann]] (1962)<ref>
{{cite journal
|author=M. Gell-Mann
|year=1962
|title=Symmetries of Baryons and Mesons
|journal=[[Physical Review]]
|volume=125 |issue=3 |pages=1067–1084
|doi=10.1103/PhysRev.125.1067
|bibcode=1962PhRv..125.1067G
}}</ref>
| discovered      =
e<sup>+</sup>e<sup>−</sup> &rarr; Y(9.46) &rarr; 3g: 1978 at [[DESY#DORIS III|DORIS]] ([[DESY]]) by [[PLUTO experiments]] (see diagram 1 and recollection<ref name="SMY">
{{cite journal
|author=B.R. Stella and H.-J. Meyer
|year=2011
|title=Y(9.46 GeV) and the gluon discovery (a critical recollection of PLUTO results)
|journal=[[European Physical Journal H]]
|volume=36 |issue=2 |pages=203–243
|arxiv=1008.1869v3
|bibcode=2011EPJH...36..203S
|doi=10.1140/epjh/e2011-10029-3
}}</ref>)<br />
and <br />
e<sup>+</sup>e<sup>−</sup> &rarr; q{{overline|q}}g: 1979 at [[PETRA]] ([[DESY]]) by [[TASSO]], [[MARK-J]], [[JADE particle detector|JADE]] and [[PLUTO dectector|PLUTO experiment]]s (see diagram 2 and review<ref name="SOE">
{{cite journal
|author=P. Söding
|year=2010
|title=On the discovery of the gluon
|journal=[[European Physical Journal H]]
|volume=35 |issue=1 |pages=3–28
|bibcode=2010EPJH...35....3S
|doi=10.1140/epjh/e2010-00002-5
}}</ref>)
| symbol          = g
| mass            = {{nowrap|{{val|0|ul=MeV/c2}} (Theoretical value)}}<ref name="pdg"/><br>{{nowrap|< {{val|0.0002|u=eV/c2}} (Experimental limit)}}<ref>
{{cite journal
|author=F. Yndurain
|year=1995
|title=Limits on the mass of the gluon
|journal=[[Physics Letters B]]
|volume=345  |issue=4 |page=524
|bibcode=1995PhLB..345..524Y
|doi=10.1016/0370-2693(94)01677-5
}}</ref>
| decay_time      =
| decay_particle  =
| electric_charge = 0&nbsp;[[elementary charge|e]]<ref name="pdg">
{{cite journal
|author=W.-M. Yao ''et al.''
|year=2006
|title=Review of Particle Physics
|url=http://pdg.lbl.gov/2007/tables/gxxx.pdf
|journal=[[Journal of Physics G]]
|volume=33 |page=1
|arxiv=astro-ph/0601168
|bibcode=2006JPhG...33....1Y
|doi=10.1088/0954-3899/33/1/001
}}</ref>
| color_charge    = octet (8 [[linear independence|linearly independent]] types)
| spin            = 1
| num_spin_states =
}}
{{Standard model of particle physics}}
'''Gluons''' {{IPAc-en|ˈ|ɡ|l|uː|ɒ|n|z}} are [[elementary particle]]s that act as the exchange particles (or [[gauge boson]]s) for the [[strong interaction|strong force]] between [[quark]]s, analogous to the exchange of [[photon]]s in the [[electromagnetic force]] between two [[charged particle]]s.<ref name=HyperPhysics>{{cite web
|author=C.R. Nave
|title=The Color Force
|url=http://hyperphysics.phy-astr.gsu.edu/hbase/forces/color.html
|work=[[HyperPhysics]]
|publisher=[[Georgia State University]], Department of Physics
|accessdate=2012-04-02
}}</ref>
 
In technical terms, gluons are [[Vector boson|vector]] [[gauge boson]]s that mediate [[strong interaction]]s of [[quark]]s in [[quantum chromodynamics]] (QCD). Gluons themselves carry the [[color charge]] of the strong interaction. This is unlike the [[photon]], which mediates the [[Electromagnetic force|electromagnetic interaction]] but lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED ([[quantum electrodynamics]]).
 
== Properties ==
[[File:Feynman Diagram Y-3g.PNG|thumb|240px|right|Diagram 1: e<sup>+</sup>e<sup>−</sup> -> Y(9.46) -> 3g]]
 
The gluon is a vector boson; like the [[photon]], it has a [[spin (physics)|spin]] of 1.  While massive spin-1 particles have three polarization states, massless gauge bosons like the gluon have only two polarization states because [[gauge invariance]] requires the polarization to be transverse. In [[quantum field theory]], unbroken gauge invariance requires that gauge bosons have zero mass (experiment limits the gluon's rest mass to less than a few meV/c<sup>2</sup>). The gluon has negative intrinsic [[parity (physics)|parity]].
 
== Numerology of gluons ==
 
Unlike the single [[photon]] of QED or the three [[W and Z bosons]] of the [[weak interaction]], there are eight independent types of gluon in QCD.
 
This may be difficult to understand intuitively. [[Quark]]s carry three types of [[color charge]]; antiquarks carry three types of anticolor. Gluons may be thought of as carrying both color and anticolor, but to correctly understand how they are combined, it is necessary to consider the mathematics of color charge in more detail.
 
=== Color charge and superposition ===
In [[quantum mechanics]], the states of particles may be added according to the [[quantum superposition|principle of superposition]]; that is, they may be in a "combined state" with a ''probability'', if some particular quantity is measured, of giving several different outcomes.  A relevant illustration in the case at hand would be a gluon with a color state described by:
 
:<math>(r\bar{b}+b\bar{r})/\sqrt{2}.</math>
 
This is read as "red–antiblue plus blue–antired". (The factor of the square root of two is required for [[normalisable wave function|normalization]], a detail that is not crucial to understand in this discussion.)  If one were somehow able to make a direct measurement of the color of a gluon in this state, there would be a 50% chance of it having red-antiblue color charge and a 50% chance of blue-antired color charge.
 
=== Color singlet states ===
It is often said that the [[hadron|stable strongly interacting particles]] (Hadrons) observed in nature are "colorless", but more precisely they are in a "color singlet" state, which is mathematically analogous to a [[singlet state|''spin'' singlet state]].<ref name="Griff">
{{cite book
|author=
|year=1987
|title=Introduction to Elementary Particles
|pages=280–281
|publisher=[[John Wiley & Sons]]
|isbn=0-471-60386-4
}}</ref> Such states allow interaction with other color singlets, but not with other color states; because long-range gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.<ref name="Griff"/>
 
The color singlet state is:<ref name="Griff"/>
 
:<math>(r\bar{r}+b\bar{b}+g\bar{g})/\sqrt{3}.</math>
 
In words, if one could measure the color of the state, there would be equal probabilities of it being red-antired, blue-antiblue, or green-antigreen.
 
=== Eight gluon colors ===
<!-- the link "eight gluon types" from the article "Quark" links here -->
 
There are eight remaining independent color states, which correspond to the "eight types" or "eight colors" of gluons.  Because states can be mixed together as discussed above, there are many ways of presenting these states, which are known as the "color octet".  One commonly used list is:<ref name="Griff"/>
 
{| style="margin:auto;"
|-
|<math>(r\bar{b}+b\bar{r})/\sqrt{2}</math>
|&nbsp;&nbsp;&nbsp;
|<math>-i(r\bar{b}-b\bar{r})/\sqrt{2}</math>
|-
|<math>(r\bar{g}+g\bar{r})/\sqrt{2}</math>
|
|<math>-i(r\bar{g}-g\bar{r})/\sqrt{2}</math>
|-
|<math>(b\bar{g}+g\bar{b})/\sqrt{2}</math>
|
|<math>-i(b\bar{g}-g\bar{b})/\sqrt{2}</math>
|-
|<math>(r\bar{r}-b\bar{b})/\sqrt{2}</math>
|
|<math>(r\bar{r}+b\bar{b}-2g\bar{g})/\sqrt{6}.</math>
|}
 
These are equivalent to the [[Gell-Mann matrices]]; the translation between the two is that red-antired is the upper-left matrix entry, red-antiblue is the upper right entry, blue-antigreen is the lower middle entry, and so on.  The critical feature of these particular eight states is that they are [[linearly independent]], and also independent of the singlet state; there is no way to add any combination of states to produce any other.  (It is also impossible to add them to make r{{overline|r}}, g{{overline|g}}, or b{{overline|b}}<ref>
{{cite journal
|author=J. Baez
|title=Why are there eight gluons and not nine?
|url=http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html
|accessdate=2009-09-13
|archiveurl=
|archivedate=
}}</ref> otherwise the forbidden [[singlet state]] could also be made.) There are many other possible choices, but all are mathematically equivalent, at least equally complex, and give the same physical results.
 
=== Group theory details ===
 
Technically, QCD is a [[gauge theory]] with [[SU(3)]] gauge symmetry. Quarks are introduced as [[spinor|spinor fields]] in ''N''<sub>f</sub> [[flavour (particle physics)|flavor]]s, each in the [[fundamental representation]] (triplet, denoted '''3''') of the color gauge group, SU(3). The gluons are vector fields in the [[Adjoint representation of a Lie group|adjoint representation]] (octets, denoted '''8''') of color SU(3).  For a general [[lie group|gauge group]], the number of force-carriers (like photons or gluons) is always equal to the dimension of the adjoint representation. For the simple case of SU(''N''), the dimension of this representation is {{nowrap|''N''<sup>2</sup> − 1}}.
 
In terms of group theory, the assertion that there are no color singlet gluons is simply the statement that [[quantum chromodynamics]] has an SU(3) rather than a [[U(N)|U(3)]] symmetry. There is no known [[A priori and a posteriori|''a priori'']] reason for one group to be preferred over the other, but as discussed above, the experimental evidence supports SU(3).<ref name="Griff"/>
 
== Confinement ==
{{main|Color confinement}}
 
Since gluons themselves carry color charge, they participate in strong interactions.  These gluon-gluon interactions constrain color fields to string-like objects called "flux tubes", which exert constant force when stretched. Due to this force, [[quark]]s are [[color confinement|confined]] within [[composite particle]]s called [[hadron]]s. This effectively limits the range of the strong interaction to {{val|e=-15}} meters, roughly the size of an [[atomic nucleus]].  Beyond a certain distance, the energy of the flux tube binding two quarks increases linearly. At a large enough distance, it becomes energetically more favorable to pull a quark-antiquark pair out of the vacuum rather than increase the length of the flux tube.
 
Gluons also share this property of being confined within hadrons. One consequence is that gluons are not directly involved in the [[nuclear force]]s between hadrons. The force mediators for these are other hadrons called [[meson]]s.
 
Although in the [[normal phase of QCD]] single gluons may not travel freely, it is predicted that there exist [[hadron]]s that are formed entirely of gluons — called [[glueball]]s. There are also conjectures about other [[exotic hadron]]s in which real gluons (as opposed to [[virtual particle|virtual]] ones found in ordinary hadrons) would be primary constituents. Beyond the normal phase of QCD (at extreme temperatures and pressures), [[quark gluon plasma]] forms. In such a plasma there are no hadrons; quarks and gluons become free particles.
 
== Experimental observations ==
[[Quark]]s and gluons (colored) manifest themselves by fragmenting into more quarks and gluons, which in turn hadronize into normal (colorless) particles, correlated in jets. As shown in 1978 summer conferences<ref name="SMY"/> the [[PLUTO experiments]] at the electron-positron collider DORIS ([[DESY]]) reported the first evidence that the hadronic decays of the very narrow resonance Y(9.46) could be interpreted as [[three-jet event]] topologies produced by three gluons. Later published analyses by the same experiment confirmed this interpretation and also the spin 1 nature of the gluon<ref>
{{cite journal
|author=Ch. Berger ''et al.'' (PLUTO Collaboration)
|year=1979
|title=Jet analysis of the Y(9.46) decay into charged hadrons
|journal=[[Physics Letters B]]
|volume=82 |page=449
|bibcode=1979PhLB...82..449B
|doi=10.1016/0370-2693(79)90265-X
|issue=3–4
}}</ref><ref>
{{cite journal
|author=Ch. Berger ''et al.'' (PLUTO Collaboration)
|year=1981
|title=Topology of the Y decay
|journal=[[Zeitschrift für Physik C]]
|volume=8 |page=101
|bibcode=1981ZPhyC...8..101B
|doi=10.1007/BF01547873
|issue=2
}}</ref> (see also the recollection<ref name="SMY"/> and [[PLUTO experiments]]).
 
In summer 1979 at higher energies at the electron-positron collider [[PETRA]] ([[DESY]]) again three-jet topologies were observed, now interpreted as q{{overline|q}} gluon [[bremsstrahlung]], now clearly visible, by [[TASSO]],<ref>
{{cite journal
|author=R. Brandelik ''et al''. ([[TASSO collaboration]])
|year=1979
|title=Evidence for Planar Events in e<sup>+</sup>e<sup>−</sup> Annihilation at High Energies
|journal=[[Physics Letters B]]
|volume=86 |issue=2 |pages=243–249
|bibcode=1979PhLB...86..243B
|doi=10.1016/0370-2693(79)90830-X
}}</ref>
[[MARK-J]]<ref>
{{cite journal
|author=D.P. Barber ''et al''. (MARK-J collaboration)
|year=1979
|title=Discovery of Three-Jet Events and a Test of Quantum Chromodynamics at PETRA
|journal=[[Physical Review Letters]]
|volume=43 |page=830
|bibcode=1979PhRvL..43..830B
|doi= 10.1103/PhysRevLett.43.830
|issue=12
}}</ref>
and [[PLUTO detector|PLUTO]] experiments<ref>
{{cite journal
|author=Ch. Berger ''et al.'' (PLUTO Collaboration)
|year=1979
|title=Evidence for Gluon Bremsstrahlung in e<sup>+</sup>e<sup>−</sup> Annihilations at High Energies
|journal=[[Physics Letters B]]
|volume=86 |page=418
|bibcode=1979PhLB...86..418B
|doi=10.1016/0370-2693(79)90869-4
|issue=3–4
}}</ref> (later in 1980 also by [[JADE (particle detector)|JADE]]<ref>
{{cite journal
|author=W. Bartel ''et al.'' (JADE Collaboration)
|year=1980
|title=Observation of planar three-jet events in e<sup>+</sup>e<sup>−</sup> annihilation and evidence for gluon bremsstrahlung
|journal=[[Physics Letters B]]
|volume=91 |page=142
|bibcode=1980PhLB...91..142B
|doi=10.1016/0370-2693(80)90680-2
}}</ref>).
The spin 1 of the gluon was confirmed in 1980 by [[TASSO]]<ref>
{{cite journal
|author=R. Brandelik ''et al.'' ([[TASSO|TASSO Collaboration]])
|year=1980
|title=Evidence for a spin-1 gluon in three-jet events
|journal=[[Physics Letters B]]
|volume=97 |issue=3–4 |page=453
|bibcode=1980PhLB...97..453B
|doi=10.1016/0370-2693(80)90639-5
}}</ref> and [[PLUTO detector|PLUTO]] experiments<ref>
{{cite journal
|author=Ch. Berger ''et al.'' (PLUTO Collaboration)
|year=1980
|title=A study of multi-jet events in e<sup>+</sup>e<sup>−</sup> annihilation
|journal=[[Physics Letters B]]
|volume=97 |issue=3–4 |page=459
|bibcode=1980PhLB...97..459B
|doi=10.1016/0370-2693(80)90640-1
}}</ref> (see also the review<ref name="SOE"/>). In 1991 a subsequent experiment at the [[LEP]] storage ring at [[CERN]] again confirmed this result.<ref>
{{cite journal
|author=G. Alexander ''et al.'' ([[OPAL detector|OPAL Collaboration]])
|year=1991
|title=Measurement of Three-Jet Distributions Sensitive to the Gluon Spin in e<sup>+</sup>e<sup>−</sup> Annihilations at √s = 91 GeV
|journal=[[Zeitschrift für Physik C]]
|volume=52 |issue=4 |page=543
|bibcode=1991ZPhyC..52..543A
|doi=10.1007/BF01562326
}}</ref>
 
The gluons play an important role in the elementary strong interactions between [[quark]]s and gluons, described by QCD and studied particularly at the electron-proton collider [[HERA]] at [[DESY]]. The number and momentum distribution of the gluons in the [[proton]] (gluon density) have been measured by two experiments, [[H1 (particle detector)|H1]] and [[ZEUS]],<ref>
{{cite journal
|author=L. Lindeman (H1 and ZEUS collaborations)
|year=1997
|title=Proton structure functions and gluon density at HERA
|journal=[[Nuclear Physics B Proceedings Supplements]]
|volume=64 |pages=179–183
|bibcode=1998NuPhS..64..179L
|doi=10.1016/S0920-5632(97)01057-8
}}</ref> in the years 1996 till today (2012). The gluon contribution to the proton spin has been studied by the [[HERMES experiment]] at [[HERA]].<ref>http://www-hermes.desy.de</ref> The gluon density in the [[photon]] (when behaving hadronically) has also been measured.<ref>
{{cite journal
|author=C. Adloff ''et al''. (H1 collaboration)
|year=1999
|title=Charged particle cross sections in the photoproduction and extraction of the gluon density in the photon
|journal=[[European Physical Journal C]]
|volume=10 |pages=363–372
|arxiv=hep-ex/9810020
|bibcode=1999EPJC...10..363H
|doi=10.1007/s100520050761
}}</ref>
 
[[Color confinement]] is verified by the failure of [[free quark]] searches (searches of fractional charges). [[Quark]]s are normally produced in pairs (quark + antiquark) to compensate the quantum color and flavor numbers; however at [[Fermilab]] single production of [[top quark]]s has been shown.<ref>
{{cite web
|author=M. Chalmers
|date=6 March 2009
|title=Top result for Tevatron
|url=http://physicsworld.com/cws/article/news/38140
|work=[[Physics World]]
|accessdate=2012-04-02
}}</ref> No [[glueball]] has been demonstrated.
 
[[Deconfinement]] was claimed in 2000 at [[CERN]] SPS<ref>
{{cite journal
|author=M.C. Abreu ''et al''.
|year=2000
|title=Evidence for deconfinement of quark and antiquark from the J/Ψ suppression pattern measured in Pb-Pb collisions at the CERN SpS
|journal=[[Physics Letters B]]
|volume=477 |pages=28–36
|bibcode=2000PhLB..477...28A
|doi=10.1016/S0370-2693(00)00237-9
}}</ref> in [[heavy-ion collisions]], and it implies a new state of matter: [[quark-gluon plasma]], less interacting than in the [[Atomic nucleus|nucleus]], almost as in a liquid. It was found at the [[Relativistic Heavy Ion Collider]] (RHIC) at Brookhaven in the years 2004–2010 by four contemporaneous experiments.<ref>
{{cite news
|author=D. Overbye
|date=15 February 2010
|title=In Brookhaven Collider, Scientists Briefly Break a Law of Nature
|url=http://www.nytimes.com/2010/02/16/science/16quark.html
|work=[[New York Times]]
|accessdate=2012-04-02
}}</ref> A [[quark-gluon plasma]] state has been confirmed at the [[CERN]] [[Large Hadron Collider]] (LHC) by the three experiments [[A Large Ion Collider Experiment|ALICE]], [[ATLAS]] and [[Compact Muon Solenoid|CMS]] in 2010.<ref>
{{cite press
|date=26 November 2010
|title=LHC experiments bring new insight into primordial universe
|url=http://press.web.cern.ch/press/pressreleases/releases2010/PR23.10E.html
|publisher=[[CERN]]
|accessdate=2012-04-02
}}</ref>
 
== See also ==
* [[Quark]]
* [[Hadron]]
* [[Meson]]
* [[Gauge boson]]
* [[Quark model]]
* [[Quantum chromodynamics]]
* [[Quark-gluon plasma]]
* [[Color confinement]]
* [[Glueball]]
* [[Gluon field]]
* [[Gluon field strength tensor]]
* [[Exotic hadron]]s
* [[Standard Model]]
* [[Three jet events|Three-jet events]]
* [[Deep inelastic scattering]]
 
== References ==
{{reflist}}
 
==Further reading==
*{{cite journal
|author=A. Ali and G. Kramer
|year=2011
|title=JETS and QCD: A historical review of the discovery of the quark and gluon jets and its impact on QCD
|journal=[[European Physical Journal H]]
|volume=36 |issue=2 |pages=245–326
|arxiv=1012.2288
|bibcode = 2011EPJH...36..245A
|doi=10.1140/epjh/e2011-10047-1
}}
 
{{Particles}}
 
[[Category:Bosons]]
[[Category:Gauge bosons]]
[[Category:Gluons]]
[[Category:Quantum chromodynamics]]

Latest revision as of 01:03, 8 December 2014

My name's Wendi Nyholm but everybody calls me Wendi. I'm from United States. I'm studying at the university (1st year) and I play the Bass Guitar for 5 years. Usually I choose music from the famous films ;).
I have two sister. I love Equestrianism, watching TV (Breaking Bad) and Skydiving.

Here is my blog ... Fifa Coin Generator