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Mixing of the flavour singlet and isoscalar octet vector states so that the mass eigenstates separate into nonstrange and strange flavour. In the basis $|1⟩=(u\bar{u}+d\bar{d}+s\bar{s})/\sqrt{3}$, $|8_0⟩=(2s\bar{s}-u\bar{u}-d\bar{d})/\sqrt{6}$, the determinant-one rotation to $(\omega ,\varphi )$ has angle $-\arctan (1/\sqrt{2})$. Basis phases change the quoted angle but not the flavour content.

An eight-dimensional representation. For SU(3), the adjoint octet is realized by traceless matrices, and decomposing $\bar{3}\otimes 3$ separates this traceless part from the scalar singlet.

Only the singlet $|1⟩$ and isoscalar octet member $|8_0⟩$ can mix without violating isospin: they have the same $I=I_3=S=0$ and, for the vector multiplet, the same $J^{PC}=1^{--}$. The neutral triplet member has $I=1$ and is excluded in the isospin limit.

Set $|{\psi }_a⟩=|1⟩$ and $|{\psi }_b⟩=|8_0⟩$, with precisely the phases in a. Define $|n⟩=(|u\bar{u}⟩+|d\bar{d}⟩)/\sqrt{2}$. Taking overlaps givesTherefore the source's rotation convention is satisfied byThis yields $|\omega ⟩=|n⟩$ and $|\varphi ⟩=|s\bar{s}⟩$ exactly. Reversing the octet phase changes the quoted sign, with an irrelevant compensating phase on the physical phi state; exchanging the basis order gives the complementary angle. The physical statement of ideal vector-meson mixing is the pure strange and pure nonstrange content, rather than a convention-independent sign for the angle.