Omega meson

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%.

The quark composition of the
ω
meson can be thought of as a mix between
u

u
,
d

d
and
s

s
states, but it is very nearly a pure symmetric
u

u
-
d

d
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.

${\displaystyle \omega ={\psi }_8\sin \theta +{\psi }_1\cos \theta }$,

${\displaystyle \varphi ={\psi }_8\cos \theta -{\psi }_1\sin \theta }$,

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 $\arctan \frac{1}{\sqrt{2}}\approx {35.3}^{\circ }$, which almost corresponds to the actual value calculated from the masses of 35°. Therefore, the
ω
meson is nearly a pure symmetric
u

u
-
d

d
state.