Eta and eta prime mesons

The eta (Template:Subatomic particle) and eta prime meson (Template:Subatomic particle) are isosinglet mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson (Template:Subatomic particle) and bottom eta meson (Template:Subatomic particle) are similar forms of quarkonium; they have the same spin and parity as the (light) Template:Subatomic particle 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

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 Template:Math and that of the Template:Subatomic particle is larger than the quark model can naturally explain. This "[[QCD vacuum#Eta prime meson|Template:Math puzzle]]" can be resolved by the 't Hooft instanton mechanism, whose Template:Sfrac realization is also known as the Witten–Veneziano mechanism. Specifically, in QCD, the higher mass of the Template:Math is very significant, since it is associated with the axial UTemplate:Sub(1) classical symmetry, which is explicitly broken through the chiral anomaly upon quantization; thus, although the "protected" Template:Math mass is small, the Template:Math is not.

Quark composition

The Template:Math particles belong to the "pseudo-scalar" nonet of mesons which have spin Template:Nowrap and negative parity, and Template:Math and Template:Math have zero total [[Isospin|isospin, Template:Mvar]], and zero strangeness, and hypercharge. Each quark which appears in an Template:Math 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

${\mathrm{\eta }}_1=\frac{1}{\sqrt{3}}\left(\mathrm{u}\overline{\mathrm{u}}\mathrm{+}\mathrm{d}\overline{\mathrm{d}}\mathrm{+}\mathrm{s}\overline{\mathrm{s}}\right),$

and

${\mathrm{\eta }}_8=\frac{1}{\sqrt{6}}\left(\mathrm{u}\overline{\mathrm{u}}\mathrm{+}\mathrm{d}\overline{\mathrm{d}}\mathrm{-}\mathrm{2}\mathrm{s}\overline{\mathrm{s}}\right).$

The subscripts are labels that refer to the fact that Template:MathTemplate:Sub belongs to a singlet (which is fully antisymmetrical) and Template:MathTemplate:Sub 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 Template:Nobr so that the actual quark composition is a linear combination of these formulae. That is:

$\left(\begin{array}{cc}\cos {\theta }_{\mathrm{P}}& -\sin {\theta }_{\mathrm{P}}\\ \sin {\theta }_{\mathrm{P}}& \cos {\theta }_{\mathrm{P}}\end{array}\right)\left(\begin{array}{c}{\mathrm{\eta }}_8\\ {\mathrm{\eta }}_1\end{array}\right)=\left(\begin{array}{c}\mathrm{\eta }\\ {\mathrm{\eta }}^{\prime }\end{array}\right).$

The unsubscripted name Template:Math refers to the real particle which is actually observed and which is close to the Template:MathTemplate:Sub. The Template:Math is the observed particle close to Template:MathTemplate:Sub.

The Template:Math and Template:Math particles are closely related to the better-known neutral pion Template:Math where

${\mathrm{\pi }}^0=\frac{1}{\sqrt{2}}\left(\mathrm{u}\overline{\mathrm{u}}\mathrm{-}\mathrm{d}\overline{\mathrm{d}}\right).$

In fact, Template:Math Template:MathTemplate:Sub, and Template:MathTemplate:Sub are three mutually orthogonal, linear combinations of the quark pairs Template:Subatomic particleTemplate:Subatomic particle, Template:Subatomic particleTemplate:Subatomic particle, and Template:Subatomic particleTemplate:Subatomic particle; they are at the centre of the pseudo-scalar nonet of mesons with all the main quantum numbers equal to zero.

η′ meson

The η′ meson (Template:Subatomic particle) is a flavor SU(3) singlet, unlike the Template:Subatomic particle. It is a different superposition of the same quarks as the eta meson (Template:Subatomic particle), 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, $\mathrm{𝟛}\times \overline{\mathrm{𝟛}}=\mathrm{𝟙}+\mathrm{𝟠}$, where 1 corresponds to η₁ before s light quark mixing yields Template:Subatomic particle.

See also

• List of mesons
• Quarkonium
• Special unitary group

External links

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