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

Abstract

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

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