Non-strange non-baryonic states are eigenstates of G-parity

karlzr

It is said that all non-strange non-baryonic states are eigenstates of G-parity. And all members of an isospin multiplet have the same eigenvalue. Can anyone give me a proof to these two statements, or show me where I can find one?
In addition, the composite state consisting of [itex]K^{+}K^{-}[/itex] should be an eigenstate of G, according to the first statement. But after applying [itex]G=e^{-i\pi I_y}C[/itex] to [itex]K^+=u\bar{s}[/itex], we obtain [itex]\bar{K^0}=\bar{d}s[/itex]. Similarly, [itex]K^-[/itex] changes into [itex]K^0[/itex](here [itex]e^{-i\pi I_y}=e^{-i \pi \sigma_y/2}[/itex] for SU(2)) . Then how can we say [itex]K^{+}K^{-}[/itex] is an eigenstate of G?

Bill_K

In order to talk about G-parity you have to start with an eigenstate of isospin. Whereas both K⁺K^- and K⁰K⁰-bar are superpositions of I=0 and I=1.

karlzr

Do you mean [itex]K^+ K^-[/itex] and [itex]K^0\bar{K}^0[/itex] are not eigenstates of G-parity? because I don't think so. Consider [itex]\pi^+ \pi^-[/itex], it can also be superposition of I=0,1,2, but the G-parity is [itex](-1)^2=1[/itex], since [itex]\pi[/itex] are eigenstate of G with eigenvalue -1.
Actually this is about a problem from Bettini's elementary particle physics, 3.20 on page 107. Here is the link:
http://books.google.com/books?id=HNc...page&q&f=false

Bill_K

Sorry, my comment was incorrect. This paper might be of help to you, especially on p 9 where they work out the G-parity of K K-bar systems.