Pion-nucleon scattering to order p4 in SU(3) heavy baryon chiral perturbation theory

Abstract

We calculate the $T$-matrices of elastic pion-nucleon ($\pi N$) scattering up to fourth order in SU(3) heavy baryon chiral perturbation theory. The baryon mass in the chiral limit $M_0$ and the pertinent low-energy constants are determined by fitting to empirical $\pi N$ phase shifts below 200 MeV pion laboratory momentum in the physical region. The scattering lengths and scattering volumes are also extracted from the chiral amplitudes, and turn out to be in good agreement with those of other approaches and the available experimental values. On the basis of the various phase shifts and the threshold parameters, the convergence of the chiral expansion is analyzed in detail. A good convergence for $\pi N$ scattering observables is obtained when working up to fourth order. In addition, we extend the fit to 250 MeV pion laboratory momentum, and obtain also a good description of the empirical $S$- and $P$-wave phase shifts.