Chiral corrections to the Kroll-Ruderman theorem

Abstract

We calculate the one--loop corrections to the Kroll--Ruderman low--energy theorems for charged pion photoproduction in the framework of heavy baryon chiral perturbation theory. We predict the threshold S--wave multipole $E_{0+}$ to be $E_{0+}^{\rm thr}(γp \to π^+ n) = ( 28.2 \pm 0.6 )\cdot 10^{-3}/M_π$ and $E_{0+}^{\rm thr} (γn \toπ^- p) = ( -32.7 \pm 0.6 )\cdot 10^{-3}/M_π$, respectively, for a fixed pion--nucleon coupling constant, $g_{πN} = 13.4$. A comparison to the existing data is also given.