Baryon σ terms in SU(3) BChPT x 1/Nc
I.P. Fernando* and
J.L. Goity*: corresponding author
Published on:
February 28, 2020
Abstract
ChPT and the 1/Nc 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/Nc)=O(ξ). The physical baryon masses as well as lattice QCD baryon masses for different quark mass masses are analyzed to O(ξ3) 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 σ8N associated with the scalar density ˉuu+ˉdd−2ˉss is identified. In particular, the deviation from the tree level relation σ8N=13(2mN−mΣ−mΞ), 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 ms for better understanding the range of validity of the effective theory. The analysis presented here leads to σπN=69(10)~MeV and σπΔ=60(10)~MeV.
DOI: https://doi.org/10.22323/1.317.0061
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