Eta and eta prime mesons

Isosinglet meson made of quarks and antiquarks

Eta and eta prime mesonsComposition|

: ≈  1 6 ( u u ¯ + d d ¯ − 2 s s ¯ ) {\textstyle \mathrm {\frac {1}{\sqrt {6}}} \left(u{\bar {u}}+d{\bar {d}}-2s{\bar {s}}\right)}

: ≈  1 3 ( u u ¯ + d d ¯ + s s ¯ ) {\textstyle \mathrm {\frac {1}{\sqrt {3}}} \left(u{\bar {u}}+d{\bar {d}}+s{\bar {s}}\right)}

|

Statistics| Bosonic
Family| Mesons
Interactions| Strong, Weak, Gravitation, Electromagnetic
Symbol|

Antiparticle| Self
Discovered| Aihud Pevsner et al. (1961)
Types| 2
Mass|

: 547.862±0.018 MeV/c2[1]

: 957.78±0.06 MeV/c2[1]
Mean lifetime|

: (5.0±0.3)×10−19 s,

: (3.2±0.2)×10−21 s
Decays into|

) / (

) or

Electric charge| 0 e
Spin| 0
Isospin| 0
Hypercharge| 0
Parity| -1
C parity| +1

The eta (

) and eta prime meson (

) are isosinglet mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson (

c) and bottom eta meson (

b) are similar forms of quarkonium; they have the same spin and parity as the (light)

defined, but are made of charm quarks and bottom quarks respectively. The top quark is too heavy to form a similar meson, due to its very fast decay.

## General

[edit]

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 was leading to predictions and discoveries of new particles from symmetry considerations.[2]

The difference between the mass of the

and that of the

is larger than the quark model can naturally explain. This "

puzzle" can be resolved[3][4][5] by the 't Hooft instanton mechanism,[6] whose ⁠1/ N ⁠ realization is also known as the Witten–Veneziano mechanism.[7][8] Specifically, in QCD, the higher mass of the

is very significant, since it is associated with the axial UA(1) classical symmetry, which is explicitly broken through the chiral anomaly upon quantization; thus, although the "protected"

mass is small, the

is not.

## Quark composition

[edit]

The

particles belong to the "pseudo-scalar" nonet of mesons which have spin  J = 0  and negative parity,[9][10] and

and

have zero total isospin, I, and zero strangeness, and hypercharge. Each quark which appears in an

particle is accompanied by its antiquark, hence all the main quantum numbers are zero, and the particle overall is "flavourless".

The basic SU(3) symmetry theory of quarks for the three lightest quarks, which only takes into account the strong force, predicts corresponding particles

η 1 = 1 3 ( u u ¯ + d d ¯ + s s ¯ ) , {\displaystyle \mathrm {\eta } _{1}={\frac {1}{\sqrt {3}}}\left(\mathrm {u{\bar {u}}+d{\bar {d}}+s{\bar {s}}} \right)~,}

and

η 8 = 1 6 ( u u ¯ + d d ¯ − 2 s s ¯ ) . {\displaystyle \mathrm {\eta } _{8}={\frac {1}{\sqrt {6}}}\left(\mathrm {u{\bar {u}}+d{\bar {d}}-2s{\bar {s}}} \right)~.}

The subscripts are labels that refer to the fact that η1 belongs to a singlet (which is fully antisymmetrical) and η8 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 "mixing" of the eigenstates (with mixing angle  θP = −11.5°),[11] so that the actual quark composition is a linear combination of these formulae. That is:

( cos ⁡ θ P − sin ⁡ θ P sin ⁡ θ P cos ⁡ θ P ) ( η 8 η 1 ) = ( η η ′ ) . {\displaystyle \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)~.}

The unsubscripted name

refers to the real particle which is actually observed and which is close to the η8. The

is the observed particle close to η1.[10]

The

and

particles are closely related to the better-known neutral pion

, where

π 0 = 1 2 ( u u ¯ − d d ¯ ) . {\displaystyle \mathrm {\pi } ^{0}={\frac {1}{\sqrt {2}}}\left(\mathrm {u{\bar {u}}-d{\bar {d}}} \right)~.}

In fact,

, η1, and η8 are three mutually orthogonal, linear combinations of the quark pairs

, and

; they are at the centre of the pseudo-scalar nonet of mesons[9][10] with all the main quantum numbers equal to zero.

## η′ meson

[edit]

The η′ meson (

) is a flavor SU(3) singlet, unlike the

. It is a different superposition of the same quarks as the eta meson (

), 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,  3 × 3 ¯ = 1 + 8 {\displaystyle \mathbb {3} \times {\bar {\mathbb {3} }}=\mathbb {1} +\mathbb {8} } , where 1 corresponds to η1 before s light quark mixing yields

## See also

[edit]

* List of mesons
* Quarkonium
* Special unitary group

## References

[edit]

1. ^ a b Light Unflavored Mesons as appearing in Olive, K. A.; et al. (PDG) (2014). "Review of Particle Physics". Chinese Physics C. 38 (9): 090001. arXiv:1412.1408. Bibcode:2014ChPhC..38i0001O. doi:10.1088/1674-1137/38/9/090001. S2CID 118395784.
2. ^ Kupść, A. (2007). "What is interesting in

and

Meson Decays?". AIP Conference Proceedings. 950: 165–179\. arXiv:0709.0603. Bibcode:2007AIPC..950..165K. doi:10.1063/1.2819029. S2CID 15930194.η+and+η′+Meson+Decays?&rft.volume=950&rft.pages=165-179&rft.date=2007&rft_id=info:arxiv/0709.0603&rft_id=https://api.semanticscholar.org/CorpusID:15930194#id-name=S2CID&rft_id=info:doi/10.1063/1.2819029&rft_id=info:bibcode/2007AIPC..950..165K&rft.aulast=Kupść&rft.aufirst=A.&rfr_id=info:sid/en.wikipedia.org:Eta+and+eta+prime+mesons" class="Z3988">
3. ^ Del Debbio, L.; Giusti, L.; Pica, C. (2005). "Topological Susceptibility in SU(3) Gauge Theory". Physical Review Letters. 94 (3): 032003. arXiv:hep-th/0407052. Bibcode:2005PhRvL..94c2003D. doi:10.1103/PhysRevLett.94.032003. PMID 15698253. S2CID 930312.
4. ^ Lüscher, M.; Palombi, F. (2010). "Universality of the topological susceptibility in the SU(3) gauge theory". Journal of High Energy Physics. 2010 (9): 110. arXiv:1008.0732. Bibcode:2010JHEP...09..110L. doi:10.1007/JHEP09(2010)110. S2CID 119213800.
5. ^ Cè, M.; Consonni, C.; Engel, G.; Giusti, L. (2014). Testing the Witten–Veneziano mechanism with the Yang–Mills gradient flow on the lattice. 32nd International Symposium on Lattice Field Theory. arXiv:1410.8358. Bibcode:2014arXiv1410.8358C.
6. ^ 't Hooft, G. (1976). "Symmetry Breaking through Bell-Jackiw Anomalies". Physical Review Letters. 37 (1): 8–11\. Bibcode:1976PhRvL..37....8T. doi:10.1103/PhysRevLett.37.8.8-11&rft.date=1976&rft_id=info:doi/10.1103/PhysRevLett.37.8&rft_id=info:bibcode/1976PhRvL..37....8T&rft.aulast='t+Hooft&rft.aufirst=G.&rfr_id=info:sid/en.wikipedia.org:Eta+and+eta+prime+mesons" class="Z3988">
7. ^ Witten, E. (1979). "Current algebra theorems for the U(1) "Goldstone boson"". Nuclear Physics B. 156 (2): 269–283\. Bibcode:1979NuPhB.156..269W. doi:10.1016/0550-3213(79)90031-2.269-283&rft.date=1979&rft_id=info:doi/10.1016/0550-3213(79)90031-2&rft_id=info:bibcode/1979NuPhB.156..269W&rft.aulast=Witten&rft.aufirst=E.&rfr_id=info:sid/en.wikipedia.org:Eta+and+eta+prime+mesons" class="Z3988">
8. ^ Veneziano, G. (1979). "U(1) without instantons". Nuclear Physics B. 159 (1–2): 213–224\. Bibcode:1979NuPhB.159..213V. doi:10.1016/0550-3213(79)90332-8.1–2&rft.pages=213-224&rft.date=1979&rft_id=info:doi/10.1016/0550-3213(79)90332-8&rft_id=info:bibcode/1979NuPhB.159..213V&rft.aulast=Veneziano&rft.aufirst=G.&rft_id=https://cds.cern.ch/record/133349&rfr_id=info:sid/en.wikipedia.org:Eta+and+eta+prime+mesons" class="Z3988">
9. ^ a b The Wikipedia meson article describes the SU(3) pseudo-scalar nonet of mesons including

and

10. ^ a b c Jones, H. F. (1998). Groups, Representations and Physics. IOP Publishing. ISBN 978-0-7503-0504-4. Page 150 describes the SU(3) pseudo-scalar nonet of mesons including

and

. Page 154 defines η1 and η8 and explains the mixing (leading to

and

11. ^ Quark Model Review as appearing in Beringer, J.; et al. (PDG) (2012). "Review of Particle Physics" (PDF). Physical Review D. 86 (1): 010001. Bibcode:2012PhRvD..86a0001B. doi:10.1103/PhysRevD.86.010001.

## External links

[edit]

* Eta and Eta' meson summaries at the Particle Data Group

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