Eta and eta prime mesons#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 was leading to predictions and discoveries of new particles from symmetry considerations.

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" can be resolved by the 't Hooft instanton mechanism, whose {{sfrac|1|{{mvar| N }}}} realization is also known as the Witten–Veneziano mechanism. 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.

The {{math|{{Subatomic particle|Eta}} }} particles belong to the "pseudo-scalar" nonet of mesons which have spin {{nowrap| Total angular momentum {{=}} 0 }} and negative parity, and {{math|{{Subatomic particle|eta}} }} and {{math|{{Subatomic particle|eta prime}} }} have zero total Isospin, 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 "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

:$\backslash mathrm\{\backslash eta\}\_1\; =\; \backslash frac\{1\}\{\backslash sqrt\; 3\}\; \backslash left(\; \backslash mathrm\{\; u\backslash bar\{u\}\; +\; d\backslash bar\{d\}\; +\; s\backslash bar\{s\}\; \}\; \backslash right)\; ~,$

and

:$\backslash mathrm\{\backslash eta\}\_8\; =\; \backslash frac\{1\}\{\backslash sqrt\; 6\}\; \backslash left(\; \backslash mathrm\{\; u\backslash bar\{u\}\; +\; d\backslash bar\{d\}\; -\; 2s\backslash bar\{s\}\; \}\; \backslash right)\; ~.$

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 "mixing" of the eigenstates (with mixing angle {{nobr| {{mvar|θ}}{{sub|P}} {{=}} −11.5°),}} so that the actual quark composition is a linear combination of these formulae. That is:

:$\backslash left(\backslash begin\{array\}\{cc\}$

\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 {{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}}.

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

:$\backslash mathrm\{\backslash pi\}^0\; =\; \backslash frac\{1\}\{\backslash sqrt\; 2\}\; \backslash left(\; \backslash mathrm\{\; u\backslash bar\{u\}\; -\; d\backslash bar\{d\}\; \}\; \backslash right)\; ~.$

In fact, {{math|{{subatomic particle|pion0}},}} {{math|η}}{{sub|1}}, and {{math|η}}{{sub|8}} are three 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 with all the main quantum numbers equal to zero.

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, $\backslash mathbb\{3\}\; \backslash times\; \backslash bar\{\backslash mathbb\{3\}\}\; =\; \backslash mathbb\{1\}\; +\; \backslash mathbb\{8\}$, where 1 corresponds to η₁ before s light quark mixing yields {{Subatomic particle|eta prime}}.

• List of mesons
• Quarkonium
• Special unitary group

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• [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