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Mar 16, 2021 at 20:25 comment added Adam Close to a second-order (quantum) phase transition, the correlation length of some correlation function $\xi$ diverges (equivalently the mass $\propto \xi^{-1}$ vanishes). To what collective excitations it would correspond for QCD is beyond my knowledge of the subject, unfortunately... most probably some baryon or meson I guess. But the point is that knowing that one is close to a phase transition allows for explaining the low mass, which might appear mysterious otherwise (because it is an emergent phenomenon).
Mar 16, 2021 at 15:04 comment added Mio Thanks for the interesting extension. Which energy scales come to your mind here?
Mar 16, 2021 at 11:41 comment added Adam To complement a little (although I agree with the answer): knowing the phase diagram for varying masses can also help to understand the physics of QCD at the physical value of the masses. Knowing for instance that we are close to a phase transition can help understand why some energy scale are very low (similarly to weakly broken continuous symmetry allows to understand the low mass of pions).
Mar 16, 2021 at 11:34 history answered Mio CC BY-SA 4.0