Physics:Omega meson

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Short description: Meson that is a superposition of an up quark–antiquark and a down quark–antiquark pair
Omega meson
Composition[math]\displaystyle{ \approx \frac{u\bar{u}+d\bar{d}}{\sqrt{2}} }[/math]
StatisticsBosonic
InteractionsStrong, weak, electromagnetic, gravity
Symbolω
antiparticleSelf
TheorizedYoichiro Nambu[1] (1957)
DiscoveredLawrence Berkeley National Laboratory (1961)[2][3]
Types1
Mass782.66±0.13 MeV/c2
mean lifetime(7.58±0.11)×10−23 s
Decays intoPion++Pion0+Pion- or Pion0+Gamma
electric charge0 e
Spin1
Isospin0
Hypercharge0
Parity−1
C parity−1

The omega meson (ω) is a flavourless meson formed from a superposition of an up quarkantiquark and a down quark–antiquark pair. It is part of the vector meson nonet[4][5] and mediates the nuclear force along with pions and rho mesons.

Properties

The most common decay mode for the ω meson is Pion+Pion0Pion- at 89.2±0.7%, followed by Pion0Gamma at 8.34±0.26%.[6]

Particle name Particle
symbol
Antiparticle
symbol
Quark
content
Rest mass (MeV/c2) IG JPC S C B' Mean lifetime (s) Commonly decays to

(>5% of decays)

Omega meson[6] ω(782) Self [math]\displaystyle{ \frac{u\bar{u}+d\bar{d}}{\sqrt{2}} }[/math] 782.66 ± 0.13 0 1−− 0 0 0 (7.58±0.11)×10−23 s Pion++Pion0+Pion- or
Pion0+Gamma

The quark composition of the ω meson can be thought of as a mix between up quarkup antiquark, down quarkdown antiquark and strange quarkstrange antiquark states, but it is very nearly a pure symmetric uu-dd state. This can be shown by deconstructing the wave function of the ω into its component parts. We see that the ω and ϕ mesons are mixtures of the SU(3) wave functions as follows.[7]

[math]\displaystyle{ \omega = \psi_8 \sin\theta + \psi_1 \cos\theta }[/math],
[math]\displaystyle{ \phi = \psi_8 \cos\theta - \psi_1 \sin\theta }[/math],

where

[math]\displaystyle{ \theta }[/math] is the nonet mixing angle,
[math]\displaystyle{ \psi_1 = \frac{u\overline{u} + d\overline{d} + s\overline{s}}{\sqrt{3}} }[/math] and
[math]\displaystyle{ \psi_8 = \frac{u\overline{u} + d\overline{d} - 2s\overline{s}}{\sqrt{6}} }[/math].

The mixing angle at which the components decouple completely can be calculated to be [math]\displaystyle{ \arctan\frac{1}{\sqrt{2}}\approx35.3^\circ }[/math], which almost corresponds to the actual value calculated from the masses of 35°. Therefore, the ω meson is nearly a pure symmetric uu-dd state.

See also

References

  1. Nambu, Yoichiro (April 25, 1957). "Possible Existence of a Heavy Neutral Meson". Physical Review 106 (6): 1366–1367. doi:10.1103/PhysRev.106.1366. Bibcode1957PhRv..106.1366N. 
  2. Maglić, B. C.; Alvarez, L. W.; Rosenfeld, A. H.; Stevenson, M. L. (August 14, 1961). "Evidence for a T=0 three-pion resonance". Physical Review Letters 7 (5): 178–182. doi:10.1103/physrevlett.7.178. Bibcode1961PhRvL...7..178M. 
  3. Maglich, B. (1976). "Discovery of omega meson-first neutral vector meson: one researcher's personal account - Discovery story". Advanced Experimental Physics 5: 79–105. https://inspirehep.net/files/bed57fc443ad4a089648fd0574f4d256. 
  4. Gell-Mann, M. (March 15, 1961). The Eightfold Way: A Theory of Strong Interaction Symmetry. Pasadena, CA: California Inst. of Tech., Synchrotron Laboratory. pp. 24. doi:10.2172/4008239. https://www.osti.gov/scitech/servlets/purl/4008239. 
  5. Ne'eman, Y. (August 1961). "Derivation of Strong Interactions from a Gauge Invariance". Nuclear Physics (Amsterdam: North-Ho lland Publishing Co.) 26 (2): 222–229. doi:10.1016/0029-5582(61)90134-1. Bibcode1961NucPh..26..222N. 
  6. 6.0 6.1 Zyla, P. A. (2021). "Particle listing - ω(782)". Particle Data Group. https://pdg.lbl.gov/2021/listings/rpp2021-list-omega-782.pdf. 
  7. Amsler, C.; DeGrand, T.; Krusche, B. (August 2019). "15. Quark Model". Particle Data Group. https://pdg.lbl.gov/2021/reviews/rpp2020-rev-quark-model.pdf.