Remark on the Potential Function of the Linear Sigma Model

Abstract

It is shown that the potential functions for the ordinary linear sigma model can be divided into two topographically different types depending on whether the quantity $R\equiv (m_{\sigma }/m_{\pi }{)}^2$ is greater than or less than nine. Since the Wigner-Weyl mode (R=1) and the Nambu-Goldstone mode ($R=\infty$ belong to different regions, we speculate that this classification may provide a generalization to the broken symmetry situation, which could be convenient for roughly characterizing different possible applications of the model. It is noted that a more complicated potential does not so much change this picture as add different new regions.

Comments: 26 pages, 11 figures (gzipped)