View source for Eta and eta prime mesons

{{Infobox particle
| name = Eta and eta prime mesons
| image = 
| caption = 
| num_types = 2
| composition = {{ubl
 | {{nowrap|{{Subatomic particle|eta}} : ≈ <math display="inline">\mathrm{\frac{1}{\sqrt{6}}}\left(u\bar{u} + d\bar{d} - 2s\bar{s}\right)</math>}}
 | {{nowrap|{{Subatomic particle|eta prime}} : ≈ <math display="inline">\mathrm{\frac{1}{\sqrt{3}}}\left(u\bar{u} + d\bar{d} + s\bar{s}\right)</math>}}
 }}
| statistics = [[Bosonic]]
| group = [[Meson]]s
| interaction = [[Strong interaction|Strong]], [[Weak interaction|Weak]], [[Gravity|Gravitation]], [[Electromagnetic]]
| antiparticle = Self
| status = 
| theorized = 
| discovered = [[Aihud Pevsner]] ''et al.'' (1961)
| symbol = {{Subatomic particle|eta}}, {{Subatomic particle|eta prime}}
| mass = {{nowrap|{{Subatomic particle|eta}} : {{val|547.862|0.018|ul=MeV/c2}}}}<ref name=PDG14/><br />{{nowrap|{{Subatomic particle|eta prime}} : {{val|957.78|0.06|u=MeV/c2}}}}<ref name=PDG14/>
| mean_lifetime = {{nowrap|{{Subatomic particle|eta}}: {{val|5.0|0.3|e=-19|ul=s}}}}, {{nowrap|{{Subatomic particle|eta prime}}: {{val|3.2|0.2|e=-21|u=s}}}}
| decay_particle = {{ubli
 | {{Subatomic particle|Eta}} :<br> {{nowrap|{{Subatomic particle|link=yes|Photon}} + {{Subatomic particle|link=yes|Photon}}}} or <br> {{nowrap|{{Subatomic particle|link=yes|Pion0}} + {{Subatomic particle|link=yes|Pion0}} + {{Subatomic particle|link=yes|Pion0}} or}} <br>
{{nowrap|{{Subatomic particle|link=yes|Pion+}} + {{Subatomic particle|link=yes|Pion0}} + {{Subatomic particle|link=yes|Pion-}}}}
 | {{Subatomic particle|Eta prime}} :<br>{{nowrap|{{Subatomic particle|link=yes|Pion+}}  + {{Subatomic particle|link=yes|Pion-}} + {{Subatomic particle|Eta}} or}}<br>
{{nowrap|({{Subatomic particle|link=yes|rho0}} + {{Subatomic particle|link=yes|Photon}}) / ({{Subatomic particle|link=yes|Pion+}} + {{Subatomic particle|link=yes|Pion-}} + {{Subatomic particle|link=yes|Photon}}) or}}<br>
{{nowrap|{{Subatomic particle|link=yes|Pion0}} + {{Subatomic particle|link=yes|Pion0}} + {{Subatomic particle|link=yes|Photon}}}}
 }}
| electric_charge = {{val|0|ul=e}}
| spin = 0
| strangeness = 
| charm = 
| bottomness = 
| topness = 
| isospin = 0
| hypercharge = 0
| parity = -1
| c_parity = +1
}}

The '''eta''' ({{Subatomic particle|eta}}) and '''eta prime meson''' ({{Subatomic particle|eta prime}}) are isosinglet [[meson]]s made of a mixture of [[up quark|up]], [[down quark|down]] and [[strange quark|strange]] [[quark]]s and their [[antiquark]]s. The [[charmed eta meson]] ({{Subatomic particle|charmed eta}}) and [[bottom eta meson]] ({{Subatomic particle|bottom eta}}) are similar forms of [[quarkonium]]; they have the same [[Spin (physics)|spin]] and [[parity (physics)|parity]] as the (light) {{Subatomic particle|eta}}  defined,  but are made of [[charm quark]]s and [[bottom quark]]s respectively. The [[top quark]] is too heavy to form a similar meson, due to its very fast decay.

==General==
The eta was discovered in [[pion]]–[[nucleon]] collisions at the [[Bevatron]] in 1961 by [[Aihud Pevsner]] et al. at a time when the proposal of the [[Eightfold Way (physics)|Eightfold Way]] was leading to predictions and discoveries of new particles from symmetry considerations.<ref name=Kupsc/>

The difference between the mass of the {{math|{{Subatomic particle|eta}} }} and that of the {{Subatomic particle|eta prime}} is larger than the [[quark model]] can naturally explain. This "[[QCD vacuum#Eta prime meson|{{math|{{Subatomic particle|eta}}–{{Subatomic particle|eta prime}} }} puzzle]]" can be resolved<ref name=DelDebbio/><ref name=Luscher/><ref name=Ce/> by the 't&nbsp;Hooft [[instanton]] mechanism,<ref name=Hooft/> whose {{sfrac|1|{{mvar| N }}}} realization is also known as the '''Witten–Veneziano mechanism'''.<ref name=Witten/><ref name=Veneziano/> Specifically, in QCD, the higher mass of the {{math|{{Subatomic particle|eta prime}} }} is very significant, since it is associated with the axial  U{{sub|A}}(1)  classical symmetry, which is ''explicitly broken'' through the [[chiral anomaly]] upon quantization; thus, although the "protected" {{math|{{Subatomic particle|eta}} }} mass is small, the {{math|{{Subatomic particle|eta prime}} }} is not.

==Quark composition==
The {{math|{{Subatomic particle|Eta}} }} particles belong to the "pseudo-scalar" nonet of mesons which have spin {{nowrap| [[Total angular momentum|{{mvar|J}}]] {{=}} 0 }} and negative [[Parity (physics)|parity]],<ref name=WPMeson/><ref name=Jones/> and {{math|{{Subatomic particle|eta}} }} and {{math|{{Subatomic particle|eta prime}} }} have zero total [[Isospin|isospin, {{mvar|I}}]], and zero [[strangeness]], and [[hypercharge]]. Each quark which appears in an {{math|{{Subatomic particle|eta}} }} particle is accompanied by its antiquark, hence all the main quantum numbers are zero, and  the particle overall is [[Flavour (particle physics)|"flavourless"]].

The basic [[SU(3)]] symmetry [[Particle physics and representation theory|theory of quarks]] for the three lightest quarks, which only takes into account the [[strong force]], predicts corresponding particles 
:<math> \mathrm{\eta}_1 = \frac{1}{\sqrt 3} \left( \mathrm{ u\bar{u} + d\bar{d} + s\bar{s} } \right) ~,</math>
and 
:<math>\mathrm{\eta}_8 = \frac{1}{\sqrt 6} \left( \mathrm{ u\bar{u} + d\bar{d} - 2s\bar{s} } \right) ~.</math>

The subscripts are labels that refer to the fact that {{math|η}}{{sub|1}} belongs to a singlet (which is fully antisymmetrical) and {{math|η}}{{sub|8}} is part of an octet. However, the [[electroweak interaction]] – which can transform one flavour of quark into another – causes a small but significant amount of "[[quantum superposition|mixing]]" of the [[Eigenvalues and eigenvectors|eigenstates]] (with mixing angle {{nobr| {{mvar|θ}}{{sub|P}} {{=}} −11.5°),}}<ref name=PDG/> so that the actual quark composition is a linear combination of these formulae. That is:

:<math>\left(\begin{array}{cc}
    \cos\theta_\mathrm{P} & - \sin\theta_\mathrm{P} \\
    \sin\theta_\mathrm{P} & ~~\cos\theta_\mathrm{P}
  \end{array}\right) \left(\begin{array}{c} \mathrm{\eta}_8 \\
        \mathrm{\eta}_1 \end{array}\right) =
  \left(\begin{array}{c} \mathrm{\eta} \\ \mathrm{\eta'} \end{array}\right) ~.
</math>

The unsubscripted name {{math| {{Subatomic particle|eta}} }} refers to the real particle which is actually observed and which is close to the {{math|η}}{{sub|8}}. The {{math| {{Subatomic particle|eta prime}} }} is the observed particle close to {{math|η}}{{sub|1}}.<ref name=Jones/>

The {{math|{{Subatomic particle|eta}} }} and {{math|{{Subatomic particle|eta prime}} }} particles are closely related to the better-known neutral [[pion]] {{math|{{Subatomic particle|link=yes|pion0}},}} where
:<math>\mathrm{\pi}^0 = \frac{1}{\sqrt 2} \left( \mathrm{ u\bar{u} - d\bar{d} } \right) ~.</math>

In fact, {{math|{{subatomic particle|pion0}},}} {{math|η}}{{sub|1}}, and {{math|η}}{{sub|8}} are three [[Orthogonal functions|mutually orthogonal]], linear combinations of the quark pairs {{subatomic particle|up quark}}{{subatomic particle|up antiquark}}, {{subatomic particle|down quark}}{{subatomic particle|down antiquark}}, and {{subatomic particle|strange quark}}{{subatomic particle|strange antiquark}}; they are at the centre of the pseudo-scalar nonet of mesons<ref name=WPMeson/><ref name=Jones/> with all the main quantum numbers equal to zero.

==η′ meson==
The η′ meson ({{Subatomic particle|eta prime}}) is a flavor SU(3) singlet, unlike the {{Subatomic particle|eta}}. It is a different superposition of the same quarks as the eta meson ({{Subatomic particle|eta}}), as described above, and it has a higher mass, a different decay state, and a shorter lifetime.

Fundamentally, it results from the direct sum decomposition of the approximate SU(3) flavor symmetry among the 3 lightest quarks, <math>\mathbb{3} \times \bar{\mathbb{3}} = \mathbb{1} + \mathbb{8}</math>, where '''1''' corresponds to η<sub>1</sub> before s light quark mixing yields {{Subatomic particle|eta prime}}.

==See also==
* [[List of mesons]]
* [[Quarkonium]]
* [[Special unitary group]]

==References==
{{Reflist|refs=
<ref name=PDG>[http://pdg.lbl.gov/2012/reviews/rpp2012-rev-quark-model.pdf Quark Model Review] as appearing in {{cite journal
 |last1=Beringer |first1=J.
 |author2=et al. ([[Particle Data Group|PDG]])
 |year=2012
 |title=Review of Particle Physics
 |url=http://pdg.lbl.gov/2012/reviews/rpp2012-rev-quark-model.pdf
 |journal=[[Physical Review D]]
 |volume=86 |issue=1 |pages=010001
 |bibcode= 2012PhRvD..86a0001B
 |doi= 10.1103/PhysRevD.86.010001
 |doi-access=free
 }}</ref>
<ref name=PDG14>[http://pdg.lbl.gov/2014/tables/rpp2014-tab-mesons-light.pdf Light Unflavored Mesons] as appearing in {{cite journal
 |last1=Olive |first1=K. A.
 |author2=et al. ([[Particle Data Group|PDG]])
 |year=2014
 |title=Review of Particle Physics
 |journal=[[Chinese Physics C]]
 |volume=38 |issue= 9|pages=090001
 |bibcode=2014ChPhC..38i0001O
 |doi=10.1088/1674-1137/38/9/090001
|arxiv=1412.1408
 |s2cid=118395784
 }}</ref>
<ref name=Jones>
{{cite book
 |last=Jones
 |first=H. F.
 |year=1998
 |title=Groups, Representations and Physics
 |publisher=[[IOP Publishing]]
 |isbn=978-0-7503-0504-4
 |url-access=registration
 |url=https://archive.org/details/groupsrepresenta0000jone_j8n8
 }} Page 150 describes the SU(3) pseudo-scalar nonet of mesons including {{Subatomic particle|eta}} and {{Subatomic particle|eta prime}}.  Page 154 defines η<sub>1</sub> and η<sub>8</sub> and explains the mixing (leading to {{Subatomic particle|eta}} and {{Subatomic particle|eta prime}}).
</ref>
<ref name=Kupsc>
{{cite journal
 |last1=Kupść |first1=A.
 |last2=<!-- --> |first2=<!-- -->
 |last3=<!-- --> |first3=<!-- -->
 |last4=<!-- --> |first4=<!-- -->
 |year=2007
 |title=What is interesting in {{Subatomic particle|eta}} and {{Subatomic particle|eta prime}} Meson Decays?
 |journal=[[AIP Conference Proceedings]]
 |volume=950 |pages=165–179
 |arxiv=0709.0603
 |bibcode=2007AIPC..950..165K
 |doi=10.1063/1.2819029
|s2cid=15930194
 }}</ref>
<ref name=WPMeson>The [[Meson#Isospin and charge|Wikipedia meson article]] describes the SU(3) pseudo-scalar nonet of mesons including {{Subatomic particle|eta}} and {{Subatomic particle|eta prime}}.</ref>
<ref name=Hooft>
{{cite journal
 |last1='t Hooft |first1=G.
 |year=1976
 |title=Symmetry Breaking through Bell-Jackiw Anomalies
 |journal=[[Physical Review Letters]]
 |volume=37 |issue=1 |pages=8–11
 |bibcode=1976PhRvL..37....8T
 |doi=10.1103/PhysRevLett.37.8
}}</ref>
<ref name=Witten>
{{cite journal
 |last1=Witten |first1=E.
 |year=1979
 |title=Current algebra theorems for the U(1) "Goldstone boson"
 |journal=[[Nuclear Physics B]]
 |volume=156 |issue=2 |pages=269–283
 |bibcode=1979NuPhB.156..269W
 |doi=10.1016/0550-3213(79)90031-2
}}</ref>
<ref name=Veneziano>
{{cite journal
 |last1=Veneziano |first1=G.
 |year=1979
 |title=U(1) without instantons
 |journal=[[Nuclear Physics B]]
 |volume=159 |issue=1–2 | pages=213–224
 |bibcode=1979NuPhB.159..213V
 |doi=10.1016/0550-3213(79)90332-8
|url=https://cds.cern.ch/record/133349
 }}</ref>
<ref name=DelDebbio>
{{cite journal
 |last1=Del Debbio |first1=L.
 |last2=Giusti |first2=L.
 |last3=Pica |first3=C.
 |year=2005
 |title=Topological Susceptibility in SU(3) Gauge Theory
 |journal=[[Physical Review Letters]]
 |volume=94 |issue=3 |pages=032003
 |arxiv=hep-th/0407052
 |bibcode=2005PhRvL..94c2003D
 |doi=10.1103/PhysRevLett.94.032003 
|pmid=15698253
 |s2cid=930312
 }}</ref>
<ref name=Luscher>
{{cite journal
 |last1=Lüscher |first1=M.
 |last2=Palombi |first2=F.
 |year=2010
 |title=Universality of the topological susceptibility in the SU(3) gauge theory
 |journal=[[Journal of High Energy Physics]]
 |volume=2010 |issue=9 |pages=110
 |arxiv=1008.0732
 |bibcode=2010JHEP...09..110L
 |doi=10.1007/JHEP09(2010)110
|s2cid=119213800
 }}</ref>
<ref name=Ce>
{{cite conference
 |last1=Cè |first1=M.
 |last2=Consonni |first2=C.
 |last3=Engel |first3=G.
 |last4=Giusti |first4=L.
 |year=2014
 |title=Testing the Witten–Veneziano mechanism with the Yang–Mills gradient flow on the lattice 
 |conference=32nd International Symposium on Lattice Field Theory
 |arxiv=1410.8358
|bibcode=2014arXiv1410.8358C}}</ref>
}}

==External links==
* [http://pdg.lbl.gov/2018/listings/rpp2018-list-eta.pdf Eta] and [http://pdg.lbl.gov/2018/listings/rpp2018-list-eta-prime-958.pdf Eta' meson summaries] at the Particle Data Group

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[[Category:Mesons]]