Chiral Corrections to the S-Wave Pion-Nucleon Scattering Lengths

Abstract

We calculate the chiral corrections to Weinberg's prediction for the S--wave $πN$ scattering lengths up--to--and--including order ${\cal O}(M_π^3)$ 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 ${\cal O}(M_π^3)$ result depends sensitively on certain resonance parameters which enter the calculation of the contact terms present at next--to--leading order.

8 pp, TeX, 2 figures available upon request, BUTP-93/09 and CRN 93-13