Some sources state that when the mass of a quark goes to zero, it allows for Spo

Question

Some sources state that when the mass of a quark goes to zero, it allows for Spontaneous Breaking of Chiral Symmetry and gets a constituent mass of about 200MeV.

Other sources state that when the masses of the light quarks go to zero, so does the pion mass. In this case, the explicit breaking of chiral symmetry disappears, but the spontaneous chiral symmetry breaking is triggered too.

So, in this limit, is the pion massless but their quarks carry a 200MeV mass? What is wrong, or misunderstood, here?

Explanation / Answer

You are understanding correctly. In the massless up/down quark limit, chiral symmetry is restored, and the pion becomes massless but quarks are still confined, and baryons have about the same mass as they do now. This is exactly why the idea that the pion is made of quarks is nonsense.

In the 1980s, many in the new generation sought to undo the progress of the 1960s, and willfully ignored the revolutionary work of Nambu, Sakurai, Skyrme, and others, dismissing it as pre-quark nonsense. They decided that a pion is made up of two nonrelativistic quark-objects, they called these objects "constituent quarks", and they made up force laws for these to reproduce the Hadron spectrum. Georgi and Glashow even went so far as to invent a quark-quark coupling force which was designed to lower the mass of the pion by interquark interactions!

This work is a little embarassing to read. The proper model of the pion was the much earlier one due to Nambu and Weinberg, and this is now verified thanks to numerical lattice QCD, where the mass of the quark can be tuned at will. When you tune the mass of the quarks to zero, the pion mass vanishes according to the laws of chiral peturbation theory.

The pion is a mode of oscillation of the quark chiral condensate, a material filling all of space. It is made out of quarks which are created by the independent fluctuations of the gluon field.

The gluon field completely randomizes on a Baryon scale, meaning that a quark going in a closed path larger than a proton circumference will get a completely random pick from SU(3) as its holonomy. A random gauge field will create large numbers of objects whose mass scale is much lower than this randomization scale, and in this case, the objects it creates are the light up and down quarks, and to a lesser extend strange quarks. These quarks condense in pairs in the vacuum, making a condensate whose order parameter is much like a mass term in the Dirac equation: m?

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