View source for Quarkonium

{{Short description|Meson whose constituents are a quark and its own antiquark of the same flavor}}
{{Antimatter}}
In [[particle physics]], '''quarkonium''' (from [[quark]] and -[[onium]], pl. '''quarkonia''') is a [[flavor (physics)|flavorless]] [[meson]] whose constituents are a heavy [[quark]] and its own [[antiquark]], making it both a [[neutral particle]] and its own [[antiparticle]]. The name "quarkonium" is analogous to [[positronium]], the bound state of [[electron]] and [[Positron|anti-electron]]. The particles are short-lived due to matter-antimatter [[annihilation]].

==Light quarks==
{{main|Vector meson}}<!-- {{main|Phi meson}} -->

Light quarks ([[up quark|up]], [[down quark|down]], and [[strange quark|strange]]) are much less massive than the heavier quarks, and so the physical states actually seen in experiments ([[Eta meson|η]], [[Eta meson|η′]], and [[Pion|π<sup>0</sup>]] mesons) are quantum mechanical mixtures of the light quark states. The much larger mass differences between the [[charm quark|charm]] and [[bottom quark|bottom]] quarks and the lighter quarks results in states that are well defined in terms of a quark–antiquark pair of a given flavor.

==Heavy quarks==
Quarkonia, bound state of ''charmonium'' '''('''<math>c\bar{c}</math>) and ''bottomonium'' '''('''<math>b\bar{b}</math>) pairs, are crucial probes for studying the deconfined [[Quark–gluon plasma|quark-gluon plasma]] created in [[Heavy-Ion collision|ultra-relativistic heavy-ion]] collisions.<ref>{{Cite report |url=http://dx.doi.org/10.2172/1118865 |title=J/Ψ Suppression By Quark-Gluon Plasma Formation |last1=Matsui |first1=T. |last2=Satz |first2=H. |date=1986-06-01 |publisher=Office of Scientific and Technical Information (OSTI)|doi=10.2172/1118865 }}</ref> The <math>\psi</math> and <math>\Upsilon</math> families provide direct evidence of the quark structure of [[Hadron|hadrons]], support the [[Quark–gluon plasma|quark-gluon]] picture of [[perturbative quantum chromodynamics]] (QCO), and help determine the QCD scale parameter <math>\Lambda</math>. Due to the high mass of the [[top quark]], direct observation of ''toponium'' (<math>t\bar{t}</math>) is exceedingly challenging as the top quark decays through the [[electroweak interaction]] before a bound state can form. The dissociation temperature of quarkonium states depends on their binding energy, with strongly bound states like <math>J/\psi</math> and <math>\Upsilon(1S)</math> melting at higher temperatures compared to loosely bound states such as <math>\psi(2S)</math>, <math>\chi_c</math> for the charmonium family, and <math>\Upsilon(2S)</math>, <math>\Upsilon(3S)</math> for bottomonia. This sequential dissociation process enables the use of quarkonium dissociation probabilities to estimate the medium temperature, assuming quarkonium dissociation is the primary mechanism involved.<ref>{{Cite journal |last1=Digal |first1=S. |last2=Petreczky |first2=P. |last3=Satz |first3=H. |date=2001-10-08 |title=Quarkonium feed-down and sequential suppression |url=http://dx.doi.org/10.1103/physrevd.64.094015 |journal=Physical Review D |volume=64 |issue=9 |page=094015 |doi=10.1103/physrevd.64.094015 |issn=0556-2821|arxiv=hep-ph/0106017 |bibcode=2001PhRvD..64i4015D }}</ref> 

=== Charmonium{{anchor|Charmonium_anchor}} ===
{{See also|J/ψ meson}}
[[File:Quark structure charmonium.svg|thumb|Charmonium]]
In the following table, the same particle can be named with the [[spectroscopic notation]] or with its mass. In some cases excitation series are used: ψ′ is the first excitation of ψ (which, for historical reasons, is called {{SubatomicParticle|J/psi}} particle); ψ″ is a second excitation, and so on. That is, names in the same cell are synonymous.

Some of the states are predicted, but have not been identified; others are unconfirmed. The quantum numbers of the [[X(3872)]] particle have been measured recently by the LHCb experiment at CERN.<ref>{{cite journal
 |last1=Aaij |first1=R.
 |collaboration=LHCb collaboration
 |display-authors=etal
 |date=2013
 |title=Determination of the X(3872) meson quantum numbers
 |journal=[[Physical Review Letters]]
 |volume=110 |issue=22 |pages=222001
 |arxiv=1302.6269
 |bibcode=2013PhRvL.110v2001A
 |doi=10.1103/PhysRevLett.110.222001
 |pmid=23767712|s2cid=11478351
 }}</ref> This measurement shed some light on its identity, excluding the third option among the three envisioned, which are:
* a charmonium hybrid state
* a {{SubatomicParticle|D0}} {{SubatomicParticle|AntiD*0}} molecule
* a candidate for the 1<sup>1</sup>D<sub>2</sub> state

In 2005, the [[BaBar experiment]] announced the discovery of a new state: [[Y(4260)]].<ref>
{{cite web
 |date=6 July 2005
 |title=A new particle discovered by BaBar experiment
 |url=http://www.infn.it/news/newsen.php?id=351
 |publisher=[[Istituto Nazionale di Fisica Nucleare]]
 |access-date=2010-03-06
}}</ref><ref>
{{cite journal
 |last1=Aubert |first1=B.
 |collaboration=[[BaBar experiment|BaBar Collaboration]]
 |display-authors=etal
 |year=2005
 |title=Observation of a broad structure in the &pi;<sup>+</sup>&pi;<sup>−</sup>J/&psi; mass spectrum around {{val|4.26|u=GeV/c2}}
 |journal=[[Physical Review Letters]]
 |volume=95 |issue=14 |pages=142001
 |arxiv=hep-ex/0506081
 |bibcode = 2005PhRvL..95n2001A
 |doi=10.1103/PhysRevLett.95.142001
 |pmid=16241645
 |s2cid=32538123
 }}</ref> [[CLEO (particle detector)|CLEO]] and [[Belle experiment|Belle]] have since corroborated these observations. At first, Y(4260) was thought to be a charmonium state, but the evidence suggests more exotic explanations, such as a D "molecule", a 4-quark construct, or a hybrid [[meson]].

{| class="wikitable" style="align:center;"
|-
! width="40px" | [[Term symbol]] {{nowrap|''n''<sup>2''S''+1</sup>''L''<sub>''J''</sub>}}
! <!-- width="40px" --> | ''[[Isospin|I]]<sup>[[G-parity|G]]</sup>''(''[[Angular momentum#Angular momentum in quantum mechanics|J]]<sup>[[Parity (physics)|P]][[C-parity|C]]</sup>'')
! <!-- width="200px" --> | Particle
! mass (MeV/''c''<sup>2</sup>)<ref>{{cite web|title=c {{overline|c}} mesons (including possibly non-q{{overline|q}} states|url=http://pdglive.lbl.gov/ParticleGroup.action?node=MXXX025&init=}}</ref>
|-
| 1<sup>1</sup>S<sub>0</sub>
| 0<sup>+</sup>(0<sup>&minus;+</sup>)
| [[eta-c particle|''&eta;<sub>c</sub>'']](1''S'')
| {{val|2983.4|0.5}}
|-
| 1<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| [[J/Psi particle|''J/&psi;'']](1''S'')
| {{val|3096.900|0.006}}
|-
| 1<sup>1</sup>P<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>+&minus;</sup>)
| [[h-c particle|''h<sub>c</sub>'']](1''P'')
| {{val|3525.38|0.11}}
|-
| 1<sup>3</sup>P<sub>0</sub>
| 0<sup>+</sup>(0<sup>++</sup>)
| [[chi-c particle|''&chi;''<sub>''c''0</sub>]](1''P'')
| {{val|3414.75|0.31}}
|-
| 1<sup>3</sup>P<sub>1</sub>
| 0<sup>+</sup>(1<sup>++</sup>)
| ''χ''<sub>''c''1</sub>(1''P'')
| {{val|3510.66|0.07}}
|-
| 1<sup>3</sup>P<sub>2</sub>
| 0<sup>+</sup>(2<sup>++</sup>)
| ''χ''<sub>''c''2</sub>(1''P'')
| {{val|3556.20|0.09}}
|-
| 2<sup>1</sup>S<sub>0</sub>
| 0<sup>+</sup>(0<sup>&minus;+</sup>)
| ''η<sub>c</sub>''(2''S''), or ''{{SubatomicParticle|Charmed eta prime}}''
| {{val|3639.2|1.2}}
|-
| 2<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| ''ψ''(2S) or ''ψ''(3686)
| {{val|3686.097|0.025}}
|-
| 1<sup>1</sup>D<sub>2</sub>
| 0<sup>+</sup>(2<sup>&minus;+</sup>)
| ''η''<sub>''c''2</sub>(1''D'')
| align="center" |
|-
| 1<sup>3</sup>D<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| ''ψ''(3770)
| {{val|3773.13|0.35}}
|-
| 1<sup>3</sup>D<sub>2</sub>
| 0<sup>&minus;</sup>(2<sup>&minus;&minus;</sup>)
| ''ψ''<sub>2</sub>(1''D'')
| align="center" |
|-
| 1<sup>3</sup>D<sub>3</sub>
| 0<sup>&minus;</sup>(3<sup>&minus;&minus;</sup>)
| ''ψ''<sub>3</sub>(1''D'')<sup>[[#note3|[‡] ]]</sup>
| align="center" | 
|-
| 2<sup>1</sup>P<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>+&minus;</sup>)
| ''h<sub>c</sub>''(2''P'')<sup>[[#note3|[‡] ]]</sup>
| align="center" | 
|-
| 2<sup>3</sup>P<sub>0</sub>
| 0<sup>+</sup>(0<sup>++</sup>)
| ''χ''<sub>''c''0</sub>(2''P'')<sup>[[#note3|[‡] ]]</sup>
| align="center" | 
|-
| 2<sup>3</sup>P<sub>1</sub>
| 0<sup>+</sup>(1<sup>++</sup>)
| ''χ''<sub>''c''1</sub>(2''P'')<sup>[[#note3|[‡] ]]</sup>
| align="center" | 
|-
| 2<sup>3</sup>P<sub>2</sub>
| 0<sup>+</sup>(2<sup>++</sup>)
| ''χ''<sub>''c''2</sub>(2''P'')<sup>[[#note3|[‡] ]]</sup>
| align="center" | 
|-
| ?<sup>?</sup>?<sub>?</sub>
| 0<sup>+</sup>(1<sup>++</sup>)[[#note1|{{sup|[}}<nowiki>*</nowiki>{{sup|]}}]]
| ''X''(3872)
| {{val|3871.69|0.17}}
|-
| ?<sup>?</sup>?<sub>?</sub>
| ?<sup>?</sup>(1<sup>&minus;&minus;</sup>)<sup>[[#note2|[†] ]]</sup>
| ''Y''(4260)
| {{val|4263|+8|-9}}
|}
<small>Notes:</small>
:<small><span id="note1">[{{sub|<big>*</big>}}]</span> Needs confirmation.</small>
:<small><span id="note2">[†]</span> Interpretation as a 1<sup>&minus;&minus;</sup> charmonium state not favored.</small>
:<small><span id="note3">[‡]</span> Predicted, but not yet identified.</small>

===Bottomonium===
[[File:Quark structure bottomonium.svg|thumb|Bottomonium]]
{{See also |Upsilon meson}}
In the following table, the same particle can be named with the spectroscopic notation or with its mass.
Some of the states are predicted, but have not been identified; others are unconfirmed.

{| class="wikitable"
|-
! width="40px" | [[Term symbol]] ''n''<sup>2''S''+1</sup>''L''<sub>''J''</sub>
! <!-- width="40px" --> | ''[[Isospin|I]]<sup>[[G-parity|G]]</sup>''(''[[Angular momentum#Angular momentum in quantum mechanics|J]]<sup>[[Parity (physics)|P]][[C-parity|C]]</sup>'')
! <!-- width="200px" --> | Particle
! mass (MeV/''c''<sup>2</sup>)<ref>{{cite web|title=b {{overline|b}} mesons (including possibly non-q{{overline|q}} states|url=http://pdglive.lbl.gov/ParticleGroup.action?node=MXXX030&init=}}</ref>
|-
| 1<sup>1</sup>S<sub>0</sub>
| 0<sup>+</sup>(0<sup>&minus;+</sup>)
| {{Subatomic particle|link=yes|bottom eta}}(1S)
| {{val|9390.9|2.8}}
|-
| 1<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(1S)
| {{val|9460.30|0.26}}
|-
| 1<sup>1</sup>P<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>+&minus;</sup>)
| {{Physics particle|h|BR=b}}(1P)
| {{val|9899.3|0.8}}
|-
| 1<sup>3</sup>P<sub>0</sub>
| 0<sup>+</sup>(0<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b0}}]]}}(1P)
| {{val|9859.44|0.52}}
|-
| 1<sup>3</sup>P<sub>1</sub>
| 0<sup>+</sup>(1<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b1}}]]}}(1P)
| {{val|9892.76|0.40}}
|-
| 1<sup>3</sup>P<sub>2</sub>
| 0<sup>+</sup>(2<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b2}}]]}}(1P)
| {{val|9912.21|0.40}}
|-
| 2<sup>1</sup>S<sub>0</sub>
| 0<sup>+</sup>(0<sup>&minus;+</sup>)
| {{Subatomic particle|link=yes|bottom eta}}(2S)
|
|-
| 2<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(2S)
| {{val|10023.26|0.31}}
|-
| 1<sup>1</sup>D<sub>2</sub>
| 0<sup>+</sup>(2<sup>&minus;+</sup>)
| {{Subatomic particle|link=yes|bottom eta}}<sub>2</sub>(1D)
| 
|-
| 1<sup>3</sup>D<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(1D)
| 
|-
| 1<sup>3</sup>D<sub>2</sub>
| 0<sup>&minus;</sup>(2<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}<sub>2</sub>(1D) 
| {{val|10161.1|1.7}}
|-
| 1<sup>3</sup>D<sub>3</sub>
| 0<sup>&minus;</sup>(3<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}<sub>3</sub>(1D)
|
|-
| 2<sup>1</sup>P<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>+&minus;</sup>)
| {{Physics particle|h|BR=b}}(2P)
| {{val|10259.8|1.2}}
|-
| 2<sup>3</sup>P<sub>0</sub>
| 0<sup>+</sup>(0<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b0}}]]}}(2P)
| {{val|10232.5|0.6}}
|-
| 2<sup>3</sup>P<sub>1</sub>
| 0<sup>+</sup>(1<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b1}}]]}}(2P)
| {{val|10255.46|0.55}}
|-
| 2<sup>3</sup>P<sub>2</sub>
| 0<sup>+</sup>(2<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b2}}]]}}(2P)
| {{val|10268.65|0.55}}
|-
| 3<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(3S)
| {{val|10355.2|0.5}}
|-
| 3<sup>3</sup>P<sub>1</sub>
| 0<sup>+</sup>(1<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b1}}]]}}(3P)
|| {{val|10513.42|0.41}} (stat.) ± 0.53 (syst.)<ref name="chib3ptripletcms"/>
|-
| 3<sup>3</sup>P<sub>2</sub>
| 0<sup>+</sup>(2<sup>++</sup>)
| {{math|[[chi meson|{{Physics particle|&chi;|BR=b2}}]]}}(3P)
| {{val|10524.02|0.57}} (stat.) ± 0.53 (syst.)<ref name="chib3ptripletcms"/>
|-
| 4<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(4''S'') or {{Subatomic particle|link=yes|Upsilon}}(10580)
| {{val|10579.4|1.2}}
|-
| 5<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(5S) or {{Subatomic particle|link=yes|Upsilon}}(10860) 
| {{val|10865|8}}
|-
| 6<sup>3</sup>S<sub>1</sub>
| 0<sup>&minus;</sup>(1<sup>&minus;&minus;</sup>)
| {{Subatomic particle|link=yes|Upsilon}}(11020) 
| {{val|11019|8}}
|}

<small>'''Notes''':</small>
:<small><span id="1">[<sub><big><nowiki>*</nowiki></big></sub>]</span> Preliminary results. Confirmation needed.</small>

The {{Subatomic particle|link=yes|Upsilon}}(1S) state was discovered by the [[E288 experiment]] team, headed by [[Leon Lederman]], at [[Fermilab]] in 1977, and was the first particle containing a bottom quark to be discovered. On 21&nbsp;December 2011, the {{math|[[chi meson|{{Physics particle|&chi;|BR=b2}}]]}}(3P) state was the first particle discovered in the [[Large Hadron Collider]]; the discovery article was first posted on [[arXiv]].<ref name="arxivchib3p">{{cite journal
 |last1=Aad |first1=G.
 |display-authors=etal
 |collaboration=[[ATLAS Collaboration]]
 |year=2012
 |title=Observation of a new {{Physics particle|&chi;|BR=b}} state in radiative transitions to {{Subatomic particle|Upsilon}}(1S) and {{Subatomic particle|Upsilon}}(2S) at ATLAS
 |journal=[[Physical Review Letters]]
 |volume=108 |issue=15 |pages=152001
 |arxiv=1112.5154 |bibcode=2012PhRvL.108o2001A
 |doi=10.1103/PhysRevLett.108.152001 |pmid=22587245
 |doi-access=free
}}</ref><ref>{{cite news
 |url=https://www.bbc.co.uk/news/science-environment-16301908
 |title=LHC reports discovery of its first new particle
 |author=Jonathan Amos
 |publisher=[[BBC]]
 |date=2011-12-22 |df=dmy-all
}}</ref> In April 2012, [[D0 experiment|Tevatron's DØ experiment]] confirmed the result in a paper published in ''[[Physical Review D]]''.<ref>{{cite magazine |url=http://www.symmetrymagazine.org/breaking/2012/04/09/tevatron-experiment-confirms-lhc-discovery-of-chi-b-p3-particle/ |title=Tevatron experiment confirms LHC discovery of Chi-b (P3) particle |magazine=Symmetry |date=2012-04-09 |df=dmy-all}}</ref><ref>{{cite web |url=http://www-d0.fnal.gov/Run2Physics/WWW/results/final/B/B12A/B12A.pdf |title=Observation of a narrow mass state decaying into ϒ(1S) + γ in pp collisions at 1.96&nbsp;TeV |website=www-d0.fnal.gov}}</ref>
The ''J'' = 1 and ''J'' = 2 states were first resolved by the [[CMS experiment]] in 2018.<ref name="chib3ptripletcms">{{cite journal
 |last1=Sirunyan |first1=A. M. |display-authors=etal
 |collaboration=[[CMS experiment|CMS Collaboration]]
 |year=2018
 |title=Observation of the {{Physics particle|&chi;|BR=b1}}(3P) and {{Physics particle|&chi;|BR=b2}}(3P) and measurement of their masses
 |journal=[[Physical Review Letters]]
 |volume=121 |issue=9 |page=092002 |arxiv=1805.11192
 |bibcode=2018PhRvL.121i2002S
 |doi=10.1103/PhysRevLett.121.092002 |pmid=30230889 |doi-access=free
}}</ref>

===Toponium===
{{main|Theta meson}}
[[File:Quark structure toponium.svg|thumb|Toponium]]

'''Toponium''' is a hypothetical bound state of a top quark (<math>t</math>) and its antiparticle, the top antiquark (<math>\bar{t}</math>).<ref>{{Citation |last=Martin |first=André |title=Toponium Physics |date=1988 |work=Quarks, Leptons, and Their Constituents |pages=447–477 |url=http://dx.doi.org/10.1007/978-1-4613-0889-8_11 |access-date=2024-06-08 |place=Boston, MA |publisher=Springer US |doi=10.1007/978-1-4613-0889-8_11 |isbn=978-1-4612-8230-3}}</ref> While the standard gauge theory predicts the existence of the <math>t</math>-quark, to complete the third quark-lepton family, attempts to observe toponium <math>(t\bar{t})</math> have been unsuccessful, The rapid decay of the [[top quark]] and the large spread in beam energy present significant experimental challenges.<ref>{{Cite web |last=W. Buchmuller(CERN), Andre Martin(CERN), Johann H. Kuhn(Munich, Max Planck Inst.), F. Richard(Orsay, LAL), P. Roudeau (Orsay, LAL) |date=1985 |title=TOPONIUM PHYSICS AT LEP |url=https://cds.cern.ch/record/165437/files/cer-000076804.pdf}}</ref><ref>{{Cite journal |last1=Fuks |first1=Benjamin |last2=Hagiwara |first2=Kaoru |last3=Ma |first3=Kai |last4=Zheng |first4=Ya-Juan |date=2021-08-20 |title=Signatures of toponium formation in LHC run 2 data |journal=Physical Review D |volume=104 |issue=3 |pages=034023 |doi=10.1103/PhysRevD.104.034023 |issn=2470-0010|arxiv=2102.11281 |bibcode=2021PhRvD.104c4023F }}</ref> Despite this, searches continue through indirect methods, such as detecting specific decay products or anomalies indicating top quark pairs. Studying toponium decays offers a promising approach to search for Higgs particles with masses up to around 70 GeV, while similar searches in bottomonium decays could extend this range to 160 GeV. Additionally, studying gluon decay widths in light quarkonia can help determine the [[quantum chromodynamics]] (QCD) scale parameter.<ref>{{Cite journal |last1=Kühn |first1=J.H. |last2=Zerwas |first2=P.M. |date=September 1988 |title=The toponium scenario |url=http://dx.doi.org/10.1016/0370-1573(88)90075-0 |journal=Physics Reports |volume=167 |issue=6 |pages=321–403 |doi=10.1016/0370-1573(88)90075-0 |bibcode=1988PhR...167..321K |issn=0370-1573}}</ref>

{{expand section|date=April 2017}}

==QCD and quarkonium==
The computation of the properties of [[meson]]s in [[quantum chromodynamics]] (QCD) is a fully non-[[perturbative]] one. As a result, the only general method available is a direct computation using [[lattice QCD]] (LQCD) techniques.{{citation needed|date=August 2018}} However, for heavy quarkonium, other techniques are also effective.

The light quarks in a meson move at [[special relativity|relativistic]] speeds, since the mass of the bound state is much larger than the mass of the quark. However, the speed of the charm and the bottom quarks in their respective quarkonia is sufficiently small for relativistic effects in these states to be much reduced. It is estimated that the velocity, <math>\mathbf{v}</math>, is roughly 0.3&nbsp;times the [[speed of light]] for charmonia and roughly 0.1&nbsp;times the speed of light for bottomonia. The computation can then be approximated by an expansion in powers of <math>\mathbf{v}/c</math> and <math>v^2/c^2</math>. This technique is called [[non-relativistic QCD]] (NRQCD).

[[Non-relativistic QCD|NRQCD]] has also been quantized as a [[lattice gauge theory]], which provides another technique for LQCD calculations to use. Good agreement with the bottomonium masses has been found, and this provides one of the best non-perturbative tests of LQCD. For charmonium masses the agreement is not as good, but the LQCD community is actively working on improving their techniques. Work is also being done on calculations of such properties as widths of quarkonia states and transition rates between the states.

An early, but still effective, technique uses models of the ''effective'' potential to calculate masses of quarkonium states. In this technique, one uses the fact that the motion of the quarks that comprise the quarkonium state is non-relativistic to assume that they move in a static potential, much like non-relativistic models of the hydrogen atom. One of the most popular potential models is the so-called [[Cornell potential|''Cornell'' (or ''funnel'') ''potential'']]:<ref>{{cite journal |first1=Hee Sok |last1=Chung |first2=Jungil |last2=Lee |first3=Daekyoung |last3=Kang |year=2008 |title=Cornell potential parameters for S-wave heavy quarkonia |journal=Journal of the Korean Physical Society |volume=52 |issue=4 |pages=1151–1154 |arxiv=0803.3116 |bibcode=2008JKPS...52.1151C |s2cid=118586941 |doi=10.3938/jkps.52.1151}}</ref>

: <math>V(r) = -\frac{a}{r} + b\,r,</math>

where <math>r</math> is the effective radius of the quarkonium state, <math>a</math> and <math>b</math> are parameters.

This potential has two parts. The first part, <math>a/r</math>, corresponds to the potential induced by one-gluon exchange between the quark and its anti-quark, and is known as the ''Coulombic'' part of the potential, since its <math>1/r</math> form is identical to the well-known Coulombic potential induced by the electromagnetic force.

The second part, <math>b\,r</math>, is known as the ''confinement'' part of the potential, and parameterizes the poorly understood non-perturbative effects of QCD. Generally, when using this approach, a convenient form for the wave function of the quarks is taken, and then <math>a</math> and <math>b</math> are determined by fitting the results of the calculations to the masses of well-measured quarkonium states. Relativistic and other effects can be incorporated into this approach by adding extra terms to the potential, much as is done for the model hydrogen atom in non-relativistic quantum mechanics.

This form was derived from QCD up to <math>\mathcal{O}(\Lambda^3_\text{QCD}\,r^2)</math> by Sumino (2003).<ref>{{cite journal |first=Y. |last=Sumino |year=2003 |title=QCD potential as a "Coulomb-plus-linear" potential |journal=Physics Letters B |volume=571 |issue=3–4 |pages=173–183 |arxiv=hep-ph/0303120 |bibcode=2003PhLB..571..173S |doi=10.1016/j.physletb.2003.05.010 |s2cid=9000097}}</ref> It is popular because it allows for accurate predictions of quarkonium parameters without a lengthy lattice computation, and provides a separation between the short-distance ''Coulombic'' effects and the long-distance ''confinement'' effects that can be useful in understanding the quark / anti-quark force generated by QCD.

Quarkonia have been suggested as a diagnostic tool of the formation of the [[quark–gluon plasma]]: Both disappearance and enhancement of their formation depending on the yield of heavy quarks in plasma can occur.

==See also==
* [[OZI rule]]

==References==
{{Reflist}}

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[[Category:Mesons]]
[[Category:Onia]]