Chiral Prediction for the $\pi N$ Scattering Length $a^{-}$ to Order $\mathcal{O}(M_{\pi }^4)$

Abstract

We evaluate the S-wave pion--nucleon scattering length $a^{-}$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_{\pi }^4$. We show that the order $M_{\pi }^4$ piece of the isovector amplitude at threshold, $T_{\mathrm{thr}}^{-}$, vanishes exactly. We predict for the isovector scattering length, $0.088M_{{\pi }^{+}}^{-1}\le a^{-}\le 0.096M_{{\pi }^{+}}^{-1}$.

Comments: 5 pp, LaTeX file, 2 figures (appended as separate compressed tar file, amin.uu)