Baryon $\sigma$ terms in SU(3) BChPT x 1/Nc

Abstract

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 according to O(p) = O(1/N c ) = O(ξ). The 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.