Pion nucleon coupling constant, Goldberger-Treiman discrepancy and $\pi N$ $\sigma$ term

Abstract

We start by studying the Goldberger-Treiman discrepancy (GTd) $\Delta =(2.259\pm 0.591)$. Then we look at the $\pi N$ $\sigma$ term, with the dimensionless ratio ${\sigma }_N/2m_N=3.35$. Finally we return to predicting (via the quark model) the $\pi N$ coupling constant, with GTd $\Delta \to 0$ as $m_q\to m_N/3$.

5 pages, no figures, LaTeX; v2: corrected typo in eq. (6); v3: a discussion concerning chiral perturbation theory, and a co-author added