Calculating the Eta Particle's Composition

[yola]

Why is the eta particle written as 1/sqrt(6) *(uu(bar) + dd(bar) -2ss(bar))?
Thanks

 

[fzero]

Because that's a definite-weight state of $$SU(3)$$ flavor. And by definite-weight state I mean an eigenstate of specific $$SU(3)$$ generators (specifically what are called Casimir operators, the analog of $$\vec{J}^2$$ for $$SU(2)$$). It's analogous to working out the product states of two spin 1/2 particles, but a little bit more complicated because the algebra of $$SU(3)$$ has more generators than $$SU(2)$$.

 

[yola]

Can you please specify for me a reference to check?
Thanks

 

[fzero]

Howard Georgi, "Lie Algebras In Particle Physics" is a standard reference.

 

[yola]

Great, Thanks