I was reading Scharf's Quantum Gauge Theories: A True Ghost Story when I stumbled upon the following paragraph (p. 118):
The standard example of a gauge theory with massless gauge fields is the theory of strong interactions called quantum chromodynamics (QCD) with the Lie algebra $\mathfrak g=\mathfrak{su}(3)$. The gauge fields are the $N=8$ gluon fields which interact between themselves and with the quark fields $\psi_n$. Due to [$M_{nm}=M\delta_{mn}$] the colored quarks are degenerate in mass. But the quarks also interact weakly and, therefore, have a second quantum number called flavor. The quarks with different flavor have different masses. As we will see in the following chapter, this is due to the fact that weak interactions are mediated by massive fields.
It seems to me that the author is claiming that in the absence of weak interactions, all quarks would have the same mass. I had never seen this clam before, and I find this idea confusing to say the least.
If the weak interactions are so weak, why are quark masses so different? Shouldn't the (relative) mass differences be of order of the weak coupling constant?
The fact that the limit $g_w\to0$ is discontinuous seems unphysical to me. Is it, or should I not be worried that masses suddenly become degenerate when we set $g_w=0$?
Also, $g_w$ runs to zero at high energies, while quark masses have different running rates. How are these two facts consistent? Shouldn't quark masses unify as $g_w$ runs to zero?