Baryon Chiral Perturbation Theory combined with the 1/N c expansion is implemented for three flavors. Baryon masses, vector charges and axial vector couplings are studied to one-loop and organized according to the ξ-expansion, in which the 1/N c and the low energy power countings are linked according to 1/N c = O(ξ) = O(p). The renormalization to O(ξ 3 ) necessary for the mentioned observables is provided, along with applications to the baryon masses and axial couplings as obtained in lattice QCD calculations. A. Spin-flavor algebra and operator bases 31 1. Matrix elements of spin-flavor generators 32 2. Bases of spin-flavor composite operators 33 B. Building blocks for the effective Lagrangians 36 Interaction vertices and currents at LO 37 C. Loop integrals 38 Specific integrals 40 D. Useful operator reductions 42 E. Figures for the fits to LQCD and physical masses 43References 44

ChPT and the 1/N c expansion provide systematic frameworks for the strong interactions at low energy. A combined framework of both expansions has been developed and applied for baryons with three light-quark-flavors. The small scale expansion of the combined approach is identified as the ξ-expansion, in which the power counting of the expansions is linked accordingThe physical baryon masses as well as lattice QCD baryon masses for different quark mass masses are analyzed to O(ξ 3 ) in that framework. σ terms are addressed using the Feynman Hellmann theorem. For the nucleon, a useful connection between the deviation of the Gell-Mann-Okubo relation and the σ term σ 8N associated with the scalar densityūu +dd − 2ss is identified. In particular, the deviation from the tree level relation σ 8N = 1 3 (2m N − m Σ − m Ξ ), which gives rise to the so called σ-term puzzle, is studied in the ξ-expansion. A large correction non-analytic in ξ results for that relation, making plausible the resolution of the puzzle. Issues with the determination of the strangeness σ terms are discussed, emphasizing the need for lattice calculations at smaller m s for better understanding the range of validity of the effective theory.The analysis presented here leads to σ πN = 69(10) MeV and σ π∆ = 60(10) MeV.

No abstract

No abstract