Eta meson

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Eta and eta prime mesons
Composition η : ≈ \mathrm{\tfrac{u\bar{u} + d\bar{d} - 2s\bar{s}}{\sqrt{6}}}
η′ : ≈ \mathrm{\tfrac{u\bar{u} + d\bar{d} + s\bar{s}}{\sqrt{3}}}
Statistics Bosonic
Interactions Strong, Weak, Gravitation
Symbol η, η′
Antiparticle Self
Mass η : 547.853±0.024 MeV/c2
η′ : 957.66±0.24 MeV/c2
Mean lifetime η: (5.0±0.3)×10−19 s, η′: (3.2±0.2)×10−21 s
Decays into

η :
γ + γ or
π0 + π0 + π0 or
π+ + π0 + π
η′ :
π+ + π + η or
(ρ0 + γ) / (π+ + π + γ) or

π0 + π0 + γ
Electric charge e
Spin Integer

The eta (η) and eta prime meson (η′) are mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson (η
c
) and bottom eta meson (η
b
) are forms of quarkonium; they have the same spin and parity as the light eta but are made of charm quarks and bottom quarks respectively. The top quark is too heavy to form a similar meson (top eta meson, symbol η
t
), due to its very fast decay.

Quark composition[edit]

The η particles belong to the "pseudo-scalar" nonet of mesons which have spin J = 0 and negative parity,[1][2] and η and η′ have zero total isospin, I, and zero strangeness and hypercharge. Each quark which appears in an η particle is accompanied by its antiquark (the particle overall is "flavourless") and all the main quantum numbers are zero.

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

\eta_1 = \mathrm{\tfrac{u\bar{u} + d\bar{d} + s\bar{s}}{\sqrt{3}}}, and
\eta_8 = \mathrm{\tfrac{u\bar{u} + d\bar{d} - 2s\bar{s}}{\sqrt{6}}}.

The subscripts refer to the fact that η1 belongs to a singlet (which is fully antisymmetrical) and η8 is part of an octet. However in this case the weak and electromagnetic forces, which can transform one flavour of quark into another, cause a significant, though small, amount of "mixing" of the eigenstates (with mixing angle θP = −11.5 degrees),[3] 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} \eta_8 \\ \eta_1 \end{array}\right) = \left( \begin{array}{c} \eta \\ \eta' \end{array} \right).

The unsubscripted name η refers to the real particle which is actually observed and which is close to the η8. The η′ is the observed particle close to η1.[2]

The η and η′ particles are closely related to the better-known neutral pion π0, where

\pi^0 = \mathrm{\tfrac{u\bar{u} - d\bar{d}}{\sqrt{2}}}.

In fact π0, η1 and η8 are three mutually orthogonal linear combinations of the quark pairs uu, dd and ss; they are at the centre of the pseudo-scalar nonet of mesons[1][2] with all the main quantum numbers equal to zero.

General[edit]

The eta was discovered in pion-nucleon collisions at the Bevatron in 1961 by A. 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.[4]

The difference between the mass of the η and that of the η' is larger than the quark model can naturally explain. This "η-η' puzzle" is resolved by the Witten-Veneziano mechanism.[5][6][7]

See also[edit]

External links[edit]

References[edit]

  1. ^ a b The Wikipedia meson article describes the SU(3) pseudo-scalar nonet of mesons including η and η′.
  2. ^ a b c H. F. Jones (1998). Groups, Representations and Physics. Dirac House, Temple Back, Bristol BS1 6BE, UK: Institute of Physics Publishing. ISBN 0 7503 0504 5. . Page 150 describes the SU(3) pseudo-scalar nonet of mesons including η and η′. Page 154 defines η1 and η8 and explains the mixing (leading to η and η′).
  3. ^ Particle Data Group. "Quark Model Review". 
  4. ^ Andrzej Kupść (2007). "What is interesting in η and η′ Meson Decays?". arXiv (AIP Conference Proceedings 950): 165–179. arXiv:0709.0603. doi:10.1063/1.2819029. 
  5. ^ Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio. "Topological Susceptibility in SU(3) Gauge Theory". Phys. Rev. Lett. 94 (032003). arXiv:hep-th/0407052. doi:10.1103/PhysRevLett.94.032003. 
  6. ^ Lüscher, Martin; Palombi, Filippo (September 2010). "Universality of the topological susceptibility in the SU(3) gauge theory". Journal of High Energy Physics (JHEP). arXiv:1008.0732. doi:10.1007/JHEP09(2010)110. 
  7. ^ Cè, M; Consonni, C; Engel, G; Giusti, L (30 October 2014). "Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice". The 32nd International Symposium on Lattice Field Theory. v1. arXiv:1410.8358.