Scalar Boson Masses in Dynamically Broken Gauge Theories

Abstract

Assuming that nonperturbative QCD generates the chiral-limiting quark mass and the spinless $\pi$ and $\sigma$ mesons, we obtain a gap equation which can be solved for the scalar mass $m_{\sigma }\approx 2m_{\mathrm{qk}}$ in a manner consistent with the original Nambu-Jona-Lasinio approach. A similar relation is obtained within a hypercolor scenario between the dynamically generated component of the "hyperquark" mass and the mass of the Higgs analog.