But, that doesn't mean that the quark masses don't matter. Lattice QCD studies of a model in which pions have a mass of 300 MeV rather than 135-139 MeV, which imply heavier quark masses than those present in reality, leads to QCD behavior very different from what is observed in real life.
For example, if up and down quarks were heavier than they are, particles make of two neutrons and no protons, would be stable, something that isn't the case in the real world.
Thus, binding energy in hadrons depends upon quark masses in a quite sensitive and non-linear way.
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