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But for weak interactions such linear combinations (also for the charged pions, e.g. π^- = u'd) are still good, right? (Since they produce correct decay rates, cross ratios, for the pions.) What do you think?
well the thing is the thing is that QCD becomes strongly coupled at distances ~ 10 femtometer ~ 1/Λ_QCD s.. so we've never actually seen such a state at those energies .. indeed a bound state makes perfect sense there, but that's just not what we call a π^0 w. mass ~135MeV
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i think about it in terms of distances cause it's easier for me to visualize .. at distances<1/Λ QCD is well defined in terms of quarks and gluons .. as E->Λ the coupling becomes strong and our perturbative expansion breaks down .. (cont)
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So how do we predict the spectrum? .. well for the lighter mesons we can .. QCD has an approximate global SU(3)_L x SU(3)_R family symmetry which is also spontaneously broken to SU(3)_V by the quark condensate <qq> .. (cont)
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So the representation is good with electromagnetic and weak interactions, but with strong interactions we need to be more careful with it. I'll have to study QCD more carefully!
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