Chiral corrections to the S-wave pion-nucleon scattering lengths

We calculate the chiral corrections to Weinberg's prediction for the S-wave πN scattering lengths up-to-and-including order O(M_π³) making use of heavy baryon chiral perturbation theory. For the isospin-odd scattering length a^- these corrections are small and bring the prediction closer to the empirical value. In the case of the isospin-even a⁺ large cancellations appear so that the O(M_π³) result depends sensitively on certain resonance parameters which enter the calculation of the contact terms present at next-to-leading order.