Low--Energy Theorems for Weak Pion Production

Abstract

We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the $k^2$-dependence of the multipole $L_{0+}^{(+)}$ at threshold is given by the nucleon scalar form factor, namely $\sigma (k^2-M_{\pi }^2)/(3\pi M_{\pi }{F}_{\pi })$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.

Comments: 9 pp, TeX, 2 figures available as ps files, CRN 93-56