Sum Rules forP-Wave Pion-Nucleon Scattering Lengths from Current Algebras

Abstract

From current commutation relations and the hypothesis of partial conservation of axial-vector current, sum rules are derived relating $\pi N$ $P$-wave scattering lengths to the $S$-wave scattering lengths, the nucleon isovector magnetic moment, $g_A$, and $G_{\pi \mathrm{NN}}$.