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 $σ(k^2-M_π^2 ) /(3 πM_πF_π)$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.