Baryon masses and pion-nucleon $\sigma$-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, $\text{krig}m$. We find $\text{krig}m=749\pm 125$~MeV together with ${\sigma }_{\pi N}(0)=48\pm 10$ ~MeV. We discuss various implications of these results.

Comments: 11 pp, LaTeX, uses elsart.sty+elsart12.sty, fig. in separate file