Chiral expansion of baryon masses and $\sigma$-terms

Abstract

We analyze the octet baryon masses and the pion/kaon--nucleon $\sigma$--terms in the framework of heavy baryon chiral perturbation theory. We include {\it all} terms up-to-and-including quadratic order in the light quark masses, $m_q$. 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--nucleon $\sigma$--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, $m_0=770\pm 110$ MeV. While the corrections of order $m_q^2$ are small for the nucleon, they are still sizeable for the $\Lambda$, the $\Sigma$ and the $\Xi$. Therefore a definitive statement about the convergence of three--flavor baryon chiral perturbation can not yet be made. The strangeness content of the nucleon is $y=0.21\pm 0.20$. We also estimate the kaon--nucleon $\sigma$--terms and some two--loops contributions to the nucleon mass.

40 pp, LaTeX, uses epsf, 5 figures in massfig.uu, corrected, slight changes in the results, accepted for publication in Ann. Phys. (NY)

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• The $m^4\ln m$ Contribution to the Nucleon Mass in CHPT

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