Unitarized Heavy Baryon Chiral Perturbation Theory and the $\Delta$ Resonance in $\pi N $ Scattering

Abstract

Based on the recent phenomenological analysis done by M. Mojzis, Eur. Phys. Jour. {\bf C2} (1998) 182, of $\pi N $ scattering within the framework of Heavy Baryon Chiral Perturbation Theory we predict, after a suitable unitarization of the amplitude, the $\Delta$ resonance at $\sqrt{s} = M_\Delta = 1238 \er{22}{18}{\rm MeV} $ and with a width of $ \Gamma_\Delta = 150 \er{43}{31} {\rm MeV} $ in excellent agreement with the experimental numbers. The error bars reflect only the uncertainties in the low energy parameters as determined from an extrapolation to threshold of experimental data. We also describe satisfactorily, within errors, the phase shifts up to $\sqrt{s} \sim 1300 {\rm MeV} $.