Baryon masses and pion-nucleon $σ$-term to second order in the quark masses

Abstract

We analyze the octet baryon masses and the pion--nucleon $\sigma$--term in the framework of heavy baryon chiral perturbation theory. In contrast to previous investigations, we include {\it all} terms up-to-and-including quadratic order in the light quark masses. The pertinent low--energy constants are fixed from resonance exchange. This leaves as the only free parameter the baryon mass in the chiral limit, $\krig{m}$. We find $\krig{m} = 749 \pm 125$~MeV together with $\sigma_{\pi N} (0) = 48 \pm 10$ ~MeV. We discuss various implications of these results.