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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
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 by Goldstone's theorem we will have 3^2 - 1 = 8 goldstone bosons .. these are the light pseudoscalar mesons K^\pm π^\pm etc Since the symmetry is Global this means that they should be massless, though which is not the case .. the small masses are treated as a pertbtn .. cont
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Yes, I see it the same way, and certainly I recall reading (but did not examine details) about perturbation not applying for QCD at such energy scales.
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yea! i'll share some of what i know off the cuff in my response
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