Chiral Expansion of Baryon Masses andσ-Terms

Abstract

We analyze the octet baryon masses and the pion/kaon-nucleonσ-terms in the framework of heavy baryon chiral perturbation theory. We include all terms up-to-and-including quadratic order in the light quark masses,mq. We develop a consistent scheme to estimate low-energy constants related to scalar-isoscalar operators in the framework of resonance exchange involving one-loop graphs. The pertinent low-energy constants can only be estimated up to some finite coefficients. Including contributions from loop graphs with intermediate spin-3/2 decuplet and spin-1/2 octet states and from tree graphs including scalar mesons, we use the octet baryon masses and the pion-nucleonσ-term to fix all but one of these coefficients. Physical results are insensitive to this remaining parameter. It is also demonstrated that two-loop corrections only modify some of the subleading low-energy constants. We find for the baryon mass in the chiral limit,m=770±110 MeV. While the corrections of orderm2qare small for the nucleon, they are still sizeable for theΛ, theΣand theΞ. Therefore a definitive statement about the convergence of three-flavor baryon chiral perturbation can not yet be made. The strangeness content of the nucleon isy=0.21±0.20. We also estimate the kaon-nucleonσ-terms and some two-loops contributions to the nucleon mass.