Omega meson

Not to be confused with Omega baryon.

Omega meson

Composition	${\textstyle \approx {\frac {u{\bar {u}}+d{\bar {d}}}{\sqrt {2}}}}$
Statistics	Bosonic
Family	Mesons
Interactions	Strong, weak, electromagnetic, gravity
Symbol	ω
Antiparticle	Self
Theorized	Yoichiro Nambu[1] (1957)
Discovered	Lawrence Berkeley National Laboratory (1961)[2][3]
Types	1
Mass	782.66±0.13 MeV/c^2
Mean lifetime	(7.58±0.11)×10^−23 s
Decays into	π^+ +π^0 +π^− or π^0 +γ
Electric charge	0 e
Spin	1
Isospin	0
Hypercharge	0
Parity	−1
C parity	−1

The omega meson (ω) is a flavourless meson formed from a superposition of an up quark–antiquark 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 π⁺
π⁰
π⁻
at 89.2±0.7%, followed by π⁰
γ at 8.34±0.26%.^[6]

Particle name	Particle symbol	Antiparticle symbol	Quark content	Rest mass (MeV/c^2)	I^G	J^PC	S	C	B'	Mean lifetime (s)	Commonly decays to (>5% of decays)
Omega meson[6]	ω(782)	Self	${\textstyle {\frac {u{\bar {u}}+d{\bar {d}}}{\sqrt {2}}}}$	782.66 ± 0.13	0^−	1^−−	0	0	0	(7.58±0.11)×10^−23 s	π^+ +π^0 +π^−  or π^0 +γ

The quark composition of the ω meson can be thought of as a mix between uu, dd and ss 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]

${\displaystyle \omega =\psi _{8}\sin \theta +\psi _{1}\cos \theta }$,

${\displaystyle \phi =\psi _{8}\cos \theta -\psi _{1}\sin \theta }$,

where

${\displaystyle \theta }$ is the nonet mixing angle,

${\displaystyle \psi _{1}={\frac {u{\overline {u}}+d{\overline {d}}+s{\overline {s}}}{\sqrt {3}}}}$ and

${\displaystyle \psi _{8}={\frac {u{\overline {u}}+d{\overline {d}}-2s{\overline {s}}}{\sqrt {6}}}}$.

The mixing angle at which the components decouple completely can be calculated to be ${\textstyle \arctan {\frac {1}{\sqrt {2}}}\approx 35.3^{\circ }}$, 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

• List of mesons
• Quark model
• Vector meson

References

1. Nambu, Yoichiro (April 25, 1957). "Possible Existence of a Heavy Neutral Meson". Physical Review. 106 (6): 1366–1367. Bibcode:1957PhRv..106.1366N. doi:10.1103/PhysRev.106.1366.
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. Bibcode:1961PhRvL...7..178M. doi:10.1103/physrevlett.7.178. S2CID 121570977.
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.
4. Gell-Mann, M. (March 15, 1961). The Eightfold Way: A Theory of Strong Interaction Symmetry (Technical report). Pasadena, CA: California Inst. of Tech., Synchrotron Laboratory. p. 24. doi:10.2172/4008239. TID-12608.
5. Ne'eman, Y. (August 1961). "Derivation of Strong Interactions from a Gauge Invariance". Nuclear Physics. 26 (2). Amsterdam: North-Ho lland Publishing Co.: 222–229. Bibcode:1961NucPh..26..222N. doi:10.1016/0029-5582(61)90134-1.
6. Zyla, P. A. (2021) [2020]. "Particle listing - ω(782)" (PDF). Particle Data Group. Retrieved June 9, 2021.
7. Amsler, C.; DeGrand, T.; Krusche, B. (August 2019). "15. Quark Model" (PDF). Particle Data Group. Retrieved 9 June 2021.