Chiral Expansion of Baryon Masses andσ-Terms

Abstract

We analyze the octet baryon masses and the pionÂkaon-nucleon _-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-3Â2 decuplet and spin-1Â2 octet states and from tree graphs including scalar mesons, we use the octet baryon masses and the pion-nucleon _-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 order m 2 q are small for the nucleon, they are still sizeable for the 4, the 7 and the 5. 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 _-terms and some two-loops contributions to the nucleon mass.1997 Academic Press

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

“…Note also that an order q 3 calculation is certainly not sufficient for the σ-term. This statement is underlined by the SU(3) calculation of the baryon masses and σ-terms to order q 4 presented in [36]. The values for the LECs c 2,3,4 are in good agreement with the values found in [11], only c 2 comes out slightly larger here.…”

Decuplet baryon masses in partially quenched chiral perturbation theory

“…The masses of the octet and decuplet baryons have been investigated considerably in χPT [33,41,45,46,47,48,49]. Here we calculate the masses of the decuplet baryons to NNLO in χPT.…”

Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

“…It is a well established fact from many studies of Goldstone boson effects in baryon masses that such effects can not be neglected, see e.g. [12,28]. Of course, in these studies, large Goldstone boson loops are generated from intermediate kaons and etas whereas we are considering the case of increasing the pion mass within two-flavor QCD.…”