π−ηdegeneracy problem in gauge theories

The quark mass matrix appears to give an inadequate description of hadron symmetry breaking. Already, for pseudoscalar masses, such an approach predicts $m_{\pi }=m_{\eta }$. We show one resolution of this old problem in terms of the explicit strong dynamics and the currents of $M$-gauge models. We also discuss a second possible mechanism, applicable to a quark or $M$ model, which generates a calculable breaking as a radiative correction in one loop. This second mechanism depends only on the dynamics of the weak interactions.