The Goldberger -- Treiman Relation, $g_A$ and $g_{\pi NN}$ at $T\ne 0$

Abstract

The Goldberger-Treiman relation is shown to persist in the chiral limit at finite temperatures to order $O(T^2)$. The $T$ dependence of $g_A$ turns out to be the same as for $F_{\pi }$, $g_A(T)=g_A(0)(1-T^2/12F^2)$, while $g_{\pi NN}$ is temperature independent to this order. The baryon octet $\mathcal{D}$ and $\mathcal{F}$ couplings also behave as $F_{\pi }$ if only pions are massless in the pseudoscalar meson octet.

Comments: 7p, NSF-ITP-93-145, BUTP-93/27, PUTP-1433, November 1993