Chiral prediction for the πNS-wave scattering lengtha−to order O(Mπ4)

Abstract

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