Chiral Expansion of Baryon Masses and sigma -Terms

Publisher： Elsevier

ISSN： 0003-4916

Source： Annals of Physics, Vol.254, Iss.1, 1997-02, pp. : 192-232

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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 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, om =770±110 MeV. While the corrections of order m 2 q 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±0.20. We also estimate the kaon-nucleon sigma -terms and some two-loops contributions to the nucleon mass.