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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)
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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The Goldstones always come out massless, so could approximately represent mesons (as I understand). Would symmetry breaking not give them mass thereafter?
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breaking the symmetry doesn't give them mass, since the symmetry isn't broken by the Higgs mechanism the vev <qq> is a so called 'non perturbative' effect, it's role strictly breaks the global SU(3)xSU(3) chiral symmetry .. we can't expand a strongly coupled theory abt a vev
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However, Gell-Man showed with the "eightfold way" if we operate under the assumption that all asymptotic states are color singlets of SU(3)_c we get a spectrum that identically matches the ones we observe, in terms of quantum numbers .. cont
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In this view it seems the mesons are still expressed in terms of quarks but taking into account their color states (or net "colorless" states).
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