Quark Level Linear σ Model (LσM) via Loop Graphs(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

Abstract

First, the LσM is nonperturbatively solved via loop-order gap equations. Then the Nambu-Goldstone theorem (NGT) is expressed in LσM language. Next, the Lee null tadpole sum for this SU(2) LσM theory is shown to require N_c = 3. Then LσM s-wave chiral cancellations are studied in tree-and in loop-order. Also, vector meson dominance (VMD) is shown to follow from this LσM. Next, the scalar nonet is studied in the infinite momentum frame (IMF). Finally, the LσM is suggested as the infrared limit of nonperturbative QCD.